{
 "cells": [
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   },
   "source": [
    "# 概率论与数理统计（基于Python）"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d11bed51",
   "metadata": {
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   "source": [
    "各位同学大家好，欢迎大家来到《概率论与数理统计》的世界，这门课的实用性可能超乎大家的想象，用一句话形容《概率论与数理统计》，那就是：除了生孩子不行，其他都行。《概率论与数理统计》相对于另外两门课《高等数学》、《线性代数》来说，更倾向于解释这个世界运行的规律，研究这个世界随机的现象。\n",
    "\n",
    "本章的主要内容如下：（**内容参考：茆诗松老师的《概率论与数理统计》**）\n",
    "\n",
    "概率论专题：\n",
    "   - 随机现象与概率\n",
    "   - 条件概率、乘法公式、全概率公式与贝叶斯公式\n",
    "   - 一维随机变量及其分布函数和密度函数\n",
    "   - 一维随机变量的数字特征：期望、方差、分位数与中位数\n",
    "   - 多维随机变量及其联合分布、边际分布、条件分布\n",
    "   - 多维随机变量的数字特征：期望向量、协方差与协方差矩阵、相关系数与相关系数矩阵、条件期望\n",
    "   - 随机变量序列的收敛状态：依概率收敛、依分布收敛\n",
    "   - 大数定律\n",
    "   - 中心极限定理\n",
    "   - 数学建模案例分析：投资组合分析\n",
    "   \n",
    "数理统计专题：\n",
    "   - 总体与样本\n",
    "   - 经验分布函数与直方图\n",
    "   - 统计量与三大抽样分布\n",
    "   - 参数估计之点估计的概念\n",
    "   - 参数估计之点估计的方法：矩估计\n",
    "   - 参数估计之点估计的方法：极大似然估计\n",
    "   - 参数估计之点估计的评价：无偏性与有效性\n",
    "   - 参数估计之区间估计\n",
    "   - 假设检验之基本思想\n",
    "   - 假设检验之正态总体参数的假设检验\n",
    "   - 假设检验之似然比检验与Bootstrap方法\n",
    "   - 数学建模案例分析：量化投资的投资组合分析\n"
   ]
  },
  {
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   "id": "1b176cfa",
   "metadata": {
    "pycharm": {
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   },
   "source": [
    "## （一）概率论专题"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16a0c4dd",
   "metadata": {
    "pycharm": {
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   "source": [
    "在《概率论与数理统计》中，主要是两个部分：概率论和数理统计，这两个部分是看似相互独立但是实质是互相联系的，在后面的学习就会深有体会。现在，我们先用几个案例的引入，来讲讲为什么需要学习《概率论与数理统计》，首先是关于概率论的例子：\n",
    "\n",
    "在英语的写作中，每个英文字母的使用频率是不同的，每个英文字母的使用频率如下：\n",
    "\n",
    "$$\n",
    "\\begin{array}{cccccc}\n",
    "\\hline \\text { 字母 } & \\text { 频率 } & \\text { 字母 } & \\text { 频率 } & \\text { 字母 } & \\text { 频率 } \\\\\n",
    "\\hline E & 0.130 & D & 0.044 & G & 0.014 \\\\\n",
    "T & 0.090 & L & 0.036 & B & 0.013 \\\\\n",
    "O & 0.081 & C & 0.029 & V & 0.010 \\\\\n",
    "A & 0.078 & F & 0.028 & K & 0.004 \\\\\n",
    "N & 0.073 & U & 0.028 & X & 0.003 \\\\\n",
    "I & 0.068 & M & 0.026 & J & 0.001 \\\\\n",
    "R & 0.067 & P & 0.022 & Q & 0.001 \\\\\n",
    "S & 0.065 & Y & 0.015 & Z & 0.001 \\\\\n",
    "H & 0.058 & W & 0.015 & & \\\\\n",
    "\\hline\n",
    "\\end{array}\n",
    "$$\n",
    "\n",
    "研究发现，各个字母的使用频率是相当稳定的，我们可以**近似地看成概率**，这项研究对于信息学的编码和密码学的破译都有着重要的贡献。\n",
    "\n",
    "其次，我们再来说说数理统计的一个经典例子：女士品茶。一位女士声称自己能分喝出一杯奶茶是先加的奶还是先加的茶。一位统计学家为了证明她说的是不是真的，于是拿来十杯奶茶让她分辨，假如她能答对10杯奶茶中奶和茶混合的先后顺序，那么这位女士大概率有这项能力。但是，如果她只答对了7杯、8杯又或者是9杯呢？是否还能认为这位女士具有声称的这项能力呢？\n",
    "\n",
    "那话不多说，我们现在开始学习吧！"
   ]
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   "source": [
    "### 1.随机现象与概率"
   ]
  },
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   "source": [
    "概率论是一门研究随机现象的学科，那么关于随机现象及其相关概念的定义就十分重要了。\n",
    "\n",
    "（1）随机现象：在一定条件下,并不总是出现相同结果的现象。现实生活中，我们总是能见到不少的随机现象，如：\n",
    "   - 一位顾客在超市购买的商品件数;\n",
    "   - 一位顾客在超市排队等候付款的时间;\n",
    "   - 一颗麦穂上长着麦粒个数;\n",
    "   - 一台电视机的寿命(从开始使用到第一次维修的时间);\n",
    "   - 某城市一天内发生交通事故的次数;\n",
    "   - 测量某物理量(长度、直径等)的误差。\n",
    "   \n",
    "换一句话来说，如果事件的结果是固定的，我们可能会用另一个关系来表示，那就是《高等数学》中的确定性的函数关系。如果事件的结果是不固定的，我们希望得到每一种可能的结果出现的可能性的大小，并以此做出决策。那如何得到每一种可能的结果出现的可能性的大小呢？最简单的方式就是：做试验！\n",
    "\n",
    "（2）随机试验：很多随机现象是可以大量重复的，如抛一枚硬币可以无限次重复，不同麦穗上的麦粒数可以大量观察等，这种可重复的随机现象又称为**随机试验**，简称试验。以后常把检验一件产品看作做一次试验，观察一颗麦穗上的麦粒数也看作一次试验。但是也有很多随机现象是不能重复的，明年世界经济是增长还是衰退，一场足球赛的输贏都是不能重复的随机现象。现在介绍的概率论主要研究能大量重复的随机现象，但应十分注意的是，我们也要注意研究不能重复的随机现象。因为后者在我们经济生活中占有重要地位（经济现象很多情况下是不可重复的）。\n",
    "\n",
    "（3）样本点：认识一个随机现象首要的是能罗列出它的一切可能发生的基本结果，这里“基本结果”是指随机现象的最简单的结果，如抛一枚硬币就有两个基本结果：正面，反面；抛一颗骰子就有六个基本结果：1 点， 2 点， 3 点， 4 点， 5 点， 6 点。\n",
    "\n",
    "（4）样本空间：随机现象所有基本结果（样本点）的全体称为这个随机现象的样本空间。常用 $\\Omega=$ $\\{\\boldsymbol{\\omega}\\}$ 表示，其中元素 $\\omega$ 就是样本点。在统计学中，基本结果 $\\omega$ 将是抽样的基本单元，故基本结果又称为样本点，基本空间又称为样本空间，如抛一枚硬币的基本空间（样本空间）为\n",
    "$$\n",
    "\\Omega_{1}=\\left\\{\\omega_{0}, \\omega_{1}\\right\\}=\\{\\text { 正面, 反面 }\\}\n",
    "$$\n",
    "其中， $\\omega_{0}$ 表示正面， $\\omega_{1}$ 表示反面， 又如掷一颗骰子的基本空间为\n",
    "$$\n",
    "\\Omega_{2}=\\left\\{\\omega_{1}, \\omega_{2}, \\omega_{3}, \\omega_{4}, \\omega_{5}, \\omega_{6}\\right\\}=\\{1,2,3,4,5,6\\}\n",
    "$$\n",
    "下面用一些例子说明：\n",
    "   - “一台电视机的寿命”的基本空间可用非负实数集表示，即\n",
    "$$\n",
    "\\Omega_{4}=\\{x: x \\geqslant 0\\}\n",
    "$$\n",
    "   - “测量某物理量的误差”的基本空间常用整个实数集表示，即\n",
    "$$\n",
    "\\Omega_{5}=\\{x:-\\infty<x<\\infty\\}\n",
    "$$\n",
    "\n",
    "（5）随机事件：随机现象的某些基本结果组成的集合称为随机事件，简称事件,常用大写字母 $A, B, C$ 等表示，如在抛一颗骰子，“出现奇数点”是一个事件，它是由 1 点、 3 点、 5 点三个基本结果组成，若记这个事件为 $A$， 则有 $A=\\{1,3,5\\}$ 。\n",
    "\n",
    "例：抛两枚硬币的基本空间 $\\Omega$ 由下列四个基本结果组成:\n",
    "$$\n",
    "\\begin{array}{ll}\n",
    "\\omega_{1}=(\\text { 正, 正 }) & \\omega_{2}=(\\text { 正, 反 }) \\\\\n",
    "\\omega_{3}=(\\text { 反, 正 }) & \\omega_{4}=(\\text { 反, 反 })\n",
    "\\end{array}\n",
    "$$\n",
    "下面几个事件可用集合形式表示，也可用语言形式表示。\n",
    "$$\n",
    "\\begin{aligned}\n",
    "&A= \\text { “至少出现一个正面” }=\\left\\{\\omega_{1}, \\omega_{2}, \\omega_{3}\\right\\} . \\\\\n",
    "&B= \\text { “最多出现一个正面” }=\\left\\{\\omega_{2}, \\omega_{3}, \\omega_{4}\\right\\} \\\\\n",
    "&C= \\text { “恰好出现一个正面”} =\\left\\{\\omega_{2}, \\omega_{3}\\right\\} \\\\\n",
    "&D= \\text { “出现两面相同” }=\\left\\{\\omega_{1}, \\omega_{4}\\right\\}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "（6）事件间的关系：\n",
    "   - 事件的包含关系：设在同一个试验里有两个事件 $A$ 与 $B$，若事件 $A$ 中任一基本结果必在 $B$ 中，则称 $A$ 被包含在 $B$ 中，或 $B$ 包含 $A$， 记为 $A \\subset B$ 或 $B \\supset A$ ，这时事件 $A$ 的发生必导致事件 $B$ 的发生 。\n",
    "   - 事件的相等关系：设在同一试验里有两个事件 $A$ 与 $B$ 。若 $A$ 中任一基本结果必在 $B$ 中 $(A \\subset B)$，而 $B$ 中任一基本结果也必在 $A$ 中 $(B \\subset A)$， 则称事件 $A$ 与 $B$ 相等，记为 $A=B$， 这时 $A$ 与 $B$ 必含有相同的基本结果。\n",
    "   - 事件的互不相容性：在同一个试验里，若两个事件 $A$ 与 $B$ 没有相同的基本结果，则称事件 $A$ 与 $B$ 互不相容，或称互斥。这时事件 $A$ 与 $B$ 不可能同时发生。\n",
    "   - 必然事件与不可能事件：任一个基本空间 $\\Omega$ 都有一个最大子集(基本空间本身 $\\Omega$ )和一个最小子集，用空集符号 $\\phi$ 表示。最大子集就是必然事件，最小子集就是不可能事件。\n",
    "   \n",
    "（7）事件的运算：\n",
    "   - 对立事件：设 $A$ 为一个试验里的事件，则由不在 $A$ 中的一切基本结果组成的事件称为 $A$ 的对立事件，记为 $\\bar{A}$ 。如在掷一颗骰子的试验中，事件 $A=$ “出现偶数点”的对立事件 $\\bar{A}=$ “出现奇数点”。因为不出现偶数点必出现奇数点。\n",
    "   - 并运算：事件 $\\boldsymbol{A}$ 与 $\\boldsymbol{B}$ 的并，是由事件 $A$ 与 $B$ 中所有基本结果（相同的只计入一次)组成的一个新事件，记为 $A \\cup B$ 。在掷一颗骰子的试验中，事件 $A=$ “出现奇数点” $=\\{1,3,5\\}$ 与事件 $B=$ “出现点数不超过3“ $ =\\{1,2,3\\}$ 的并为 $A \\cup B=\\{1,2,3,5\\}$ 。 可见，事件 $A$ 与 $B$ 中重复元素只须记入并事件一次。\n",
    "   - 交运算：事件 $A$ 与 $B$ 的交，是由事件 $A$ 与 $B$ 中公共的基本结果组成的一个新事件，记为 $A \\cap B$ 或 $A B$ 。如在掷一颗骰子的试验里，$A=$ “出现奇数点” $=\\{1$, $3,5\\}$ 与事件 $B=$ “出现点数不超过3 \" $=\\{1,2,3\\}$ 的交 $A B=\\{1,3\\}$ 。 可见，若交事件 $A B$ 发生，则事件 $A$ 与 $B$ 必同时发生,反之亦然。\n",
    "   - 差运算：事件 $\\boldsymbol{A}$ 对 $\\boldsymbol{B}$ 的差，是由在事件 $A$ 中而不在事件 $B$ 中的基本结果组成的一个新事件，记为 $A-B$ 。如在掷一颗骰子试验里，事件 $A=$ “出现奇数点” $=\\{1,3,5\\}$ 对事件 $B=$ “出现点数不超过3 \" $=\\{1,2,3\\}$ 的差事件是 $A-B=\\{5\\}$ 。而 $B$ 对 $A$ 的差事件 $B-A=\\{2\\}$ 。这是两个不同的差事件。可见，差事件 $A-B$ 是表示事件 $A$ 发生而事件 $B$ 不发生这样一个事件。\n",
    "   \n",
    "（8）事件的概率：随机事件的发生是带有偶然性的。但随机事件发生的可能性还是有大小之别的,是可以设法度量的。而在生活、生产和经济活动中人们很关心一个随机事件发生的可能性大小。那如何去度量一个事件发生的可能性呢？其中一种简单的方式就是使用频率代替概率，但是这种方法有一个致命的弊端，我们使用一个例子去说明！众多科学家都对硬币正反面的概率是0.5进行了验证：\n",
    "\n",
    "$$\n",
    "\\begin{array}{lccc}\n",
    "\\hline \\text { 实验者 } & \\text { 拼硬币次数 } & \\text { 正面出现次数 } & \\text { 频率 } \\\\\n",
    "\\hline \\text { 蒲 } \\quad \\text { 丰 } & 4040 & 2048 & 0.5069 \\\\\n",
    "\\text { 皮尔逊 } & 12000 & 6019 & 0.5016 \\\\\n",
    "\\text { 皮尔逊 } & 24000 & 12012 & 0.5005 \\\\\n",
    "\\hline\n",
    "\\end{array}\n",
    "$$\n",
    "\n",
    "那究竟硬币正反面的概率是多少呢，是0.5069，还是0.5016，亦或是0.5005呢？问题的本质就是一个试验发生的频率有无限种可能，它可能取决于试验的次数、试验的环境、试验者的心态等等，但是一个事件的概率往往只有一个，因此使用频率代替概率本身就不是一件容易的事情，那如何定义概率呢？\n",
    "\n",
    "概率的公理化定义：在一个随机现象中，用来表示任一个随机事件 $A$ 发生可能性大小的实数(即比率)称为该事件的概率，记为 $P(A)$， 并规定\n",
    "   - 非负性公理：对任一事件 $A$，必有 $P(A) \\geqslant 0$ 。\n",
    "   - 正则性公理：必然事件的概率 $P(\\Omega)=1$ 。\n",
    "   - 可加性公理： 若 $A_{1}$ 与 $A_{2}$ 是两个互不相容事件(即 $\\left.A_{1} A_{2}=\\phi\\right)$, 则有 $P\\left(A_{1} \\cup A_{2}\\right)=P\\left(A_{1}\\right)+P\\left(A_{2}\\right)$\n",
    "   \n",
    "（9）事件的独立性：两个事件之间的独立性是指一个事件的发生不影响另一个事件的发生，$A=$ “第一颗骰子出现 1 点”，$B=$ “第二颗骰子出现偶数点”，\n",
    "经验事实告诉我们，第一颗骰子出现的点数不会影响第二颗骰子出现的点数，假如规定第二颗骰子出现偶数点可得奖，那么不管第一颗骰子出现什么点都不会影响你得奖的机会，这时就可以说:事件 $A$ 与 $B$ 独立。那么使用概率的语言是如何定义事件的独立性呢？\n",
    "事件的独立性的定义：对任意两个事件 $A$ 与 $B$， 若有 $P(A B)=P(A) P(B)$， 则称事件 $\\boldsymbol{A}$ 与 $\\boldsymbol{B}$ 相互独立，简称 $A$ 与$B$独立。"
   ]
  },
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   "id": "ca76dc4c",
   "metadata": {
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    }
   },
   "source": [
    "【例子】模拟频率近似概率："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "6d0ea598",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# 引入相关工具库\n",
    "import numpy as np \n",
    "import pandas as pd \n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.style.use(\"ggplot\")\n",
    "import warnings \n",
    "warnings.filterwarnings(\"ignore\")\n",
    "plt.rcParams['font.sans-serif']=['SimHei','Songti SC','STFangsong']\n",
    "plt.rcParams['axes.unicode_minus'] = False  # 用来正常显示负号\n",
    "import seaborn as sns "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "e44f8b41",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 模拟抛硬币正面的概率是否会越来越接近0.5\n",
    "import random\n",
    "def Simulate_coin(test_num):\n",
    "    random.seed(100)\n",
    "    coin_list = [1 if (random.random()>=0.5) else 0  for i in range(test_num)]   # 模拟试验结果\n",
    "    coin_frequence = np.cumsum(coin_list) / (np.arange(len(coin_list))+1)  # 计算正面为1的频率\n",
    "    plt.figure(figsize=(10,6))\n",
    "    plt.plot(np.arange(len(coin_list))+1, coin_frequence, c='blue', alpha=0.7)\n",
    "    plt.axhline(0.5,linestyle='--',c='red',alpha=0.5)\n",
    "    plt.xlabel(\"test_index\")\n",
    "    plt.ylabel(\"frequence\")\n",
    "    plt.title(str(test_num)+\" times\")\n",
    "    plt.show()\n",
    "\n",
    "Simulate_coin(test_num = 500)\n",
    "Simulate_coin(test_num = 1000)\n",
    "Simulate_coin(test_num = 5000)\n",
    "Simulate_coin(test_num = 10000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f612f5d",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### 2.条件概率、乘法公式、全概率公式与贝叶斯公式"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e460423",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "（1）条件概率：\n",
    "\n",
    "条件概率要涉及两个事件 $A$ 与 $B$ ，在事件 $B$ 已发生的条件下，事件 $A$ 再发生的概率称为条件概率，记为 $P(A \\mid B)$， 它与前面讲的事件 $A$ 的 (无条件)概率 $P(A)$ 是两个不同的概念。无条件概率与条件概率的区别在哪呢？假如事件$B$的发生不会影响事件$A$发生的概率，那么就说明这两者是相互独立的，即：$P(A \\mid B) = P(A)$，两者将没有区别；但是如果事件$B$的发生会影响到事件$A$的发生，那么$P(A \\mid B) \\not= P(A)$。\n",
    "\n",
    "举个例子：\n",
    "\n",
    "现在有两个小孩的家庭，其样本空间为 $\\Omega=\\{\\text{男男}, \\text{男女}, \\text{女男}, \\text{女女}\\}$，\n",
    "   - 事件 $A=$ “家中至少有一个女孩” 发生的概率为$P(A)=\\frac{3}{4} $\n",
    "   - 若已知事件 $B=$ “家中至少有一个男孩”发生,再求事件 $A$ 发生的概率为$P(A \\mid B)=\\frac{2}{3}$\n",
    "\n",
    "其实，为什么会出现这种情况呢？因为当我们得知事件 $B=$ “家中至少有一个男孩”已经发生的时候，我们对整个样本空间的认识就不是原来的$\\Omega=\\{\\text{男男}, \\text{男女}, \\text{女男}, \\text{女女}\\}$了，而是$\\Omega^{'}=\\{\\text{男男}, \\text{男女}, \\text{女男}\\}$\n",
    "\n",
    "可以看出，(无条件)概率 $P(A)$指的是从样本空间$\\Omega$中选出符合事件A定义的基本点的个数比例，即$P(A) = \\frac{N_A}{N_{\\Omega}}$；反观在事件 $B$ 已发生的条件下，事件 $A$ 再发生的概率$P(A \\mid B)$，由于事件$B$已经发生了，因此这个事件的样本空间由$\\Omega$缩减为$B$，因此$P(A \\mid B) = \\frac{N_{AB}}{N_B}=\\frac{\\frac{N_{AB}}{N_{\\Omega}}}{\\frac{N_B}{N_{\\Omega}}} = \\frac{P(AB)}{P(B)}$，因此我们给出条件概率的准确定义：\n",
    "\n",
    "设 $A$ 与 $B$ 是基本空间 $\\Omega$ 中的两个事件,且 $P(B)>0$,在事件 $B$ 已发生的条件下, 事件 $A$ 的条件概率 $P(A \\mid B)$ 定义为 $P(A B) / P(B)$, 即\n",
    "$$\n",
    "P(A \\mid B)=\\frac{P(A B)}{P(B)}\n",
    "$$\n",
    "其中 $P(A \\mid B)$ 也称为给定事件 $B$ 下事件 $A$ 的条件概率。\n",
    "\n",
    "<div>\n",
    "<img src=\"./images/2.png\" width=\"600\"/>\n",
    "</div>\n",
    "\n",
    "下面用一个例子说明条件概率的计算方法：某市的一项调查表明：该市有 $30 \\%$ 的学生视力有缺陷。 $7 \\%$ 的 学生听力有缺陷, $3 \\%$ 的学生视力与听力都有缺陷,记\n",
    "$$\n",
    "\\begin{aligned}\n",
    "&E=\\text { “学生视力有缺陷”},  P(E)=0.30\\\\\n",
    "&H=\\text { “学生听力有缺陷” }, \\quad P(H)=0.07 \\\\\n",
    "&E H=\\text { “学生视力与听力都有缺陷”},  \\quad P(E H)=0.03\n",
    "\\end{aligned}\n",
    "$$\n",
    "如果已知一学生听力有缺陷,那么他视力也有缺陷的概率是多少? 类似地可算得\n",
    "$$\n",
    "P(E \\mid H)=\\frac{P(E H)}{P(H)}=\\frac{0.03}{0.07}=\\frac{3}{7}\n",
    "$$\n",
    "\n",
    "（2）乘法公式：\n",
    "\n",
    "乘法公式是条件概率的第一个重要应用，他从条件概率的角度描述了两个事件A、B同时发生的概率是怎么计算的。具体公式如下：\n",
    "   - 若 $P(B)>0$, 则$P(A B)=P(B) P(A \\mid B)$\n",
    "   - 若 $P\\left(A_{1} A_{2} \\cdots A_{n-1}\\right)>0$, 则$P\\left(A_{1} A_{2} \\cdots A_{n}\\right)=P\\left(A_{1}\\right) P\\left(A_{2} \\mid A_{1}\\right) P\\left(A_{3} \\mid A_{1} A_{2}\\right) \\cdots P\\left(A_{n} \\mid A_{1} A_{2} \\cdots A_{n-1}\\right)$\n",
    "\n",
    "其实乘法公式十分好理解，如果想要计算$A$、$B$同时发生的概率，那么可以先让事件B发生，计算事件B发生的概率$P(B)$，再计算$B$发生的条件下$A$发生的概率$P(A|B)$。\n",
    "\n",
    "例子：一批零件共有 100 个, 其中有 10 个不合格品. 从中一个一个取出,求第三次才取得不合格品的概率是多少?\n",
    "\n",
    "解：以 $A_{i}$ 记事件 “第 $i$ 次取出的是不合格品”, $i=1,2,3$. 则所求概率为 $P\\left(\\bar{A}_{1} \\bar{A}_{2} A_{3}\\right)$, 由乘法公式得\n",
    "$$\n",
    "P\\left(\\bar{A}_{1} \\bar{A}_{2} A_{3}\\right)=P\\left(\\bar{A}_{1}\\right) P\\left(\\bar{A}_{2} \\mid \\bar{A}_{1}\\right) P\\left(A_{3} \\mid \\bar{A}_{1} \\bar{A}_{2}\\right)=\\frac{90}{100} \\cdot \\frac{89}{99} \\cdot \\frac{10}{98}=0.0826 .\n",
    "$$\n",
    "\n",
    "（3）全概率公式：\n",
    "\n",
    "全概率公式是计算复杂概率的一个重要方法，使一个复杂概率的计算能化繁为简。\n",
    "\n",
    "设 $B_{1}, B_{2}, \\cdots, B_{n}$ 是基本空间 $\\Omega$ 的一个分割,则对 $\\Omega$ 中任一事件 $A$,有(具体的解释如下图)\n",
    "$$\n",
    "P(A)=\\sum_{i=1}^{n} P\\left(A \\mid B_{i}\\right) P\\left(B_{i}\\right)\n",
    "$$\n",
    "\n",
    "<div>\n",
    "<img src=\"./images/3.png\" width=\"200\" align=\"middle\"/>\n",
    "<img src=\"./images/4.png\" width=\"200\" align=\"middle\"/>\n",
    "</div>\n",
    "\n",
    "例子：一批产品来自三个工厂，要求这批产品的合格率。为此对这三个工厂的产品进行调查,发现甲厂产品合格率为 $95 \\%$, 乙厂产品合格率为 $80 \\%$,丙厂产品合格率为 $65 \\%$ 。这批产品中有 $60 \\%$ 来自甲厂, $30 \\%$ 来自乙厂, 余下 $10 \\%$ 来自丙厂。\n",
    "\n",
    "若记事件 $A=$ “产品合格”, $B_{1}=$ “产品来自甲厂” $ B_{2}=$ “产品来自乙厂“, $B_{3}=$ “产品来自丙厂\"。由上述调查可知\n",
    "$$\n",
    "\\begin{gathered}\n",
    "P\\left(A \\mid B_{1}\\right)=0.95, \\quad P\\left(A \\mid B_{2}\\right)=0.80, \\quad P\\left(A \\mid B_{3}\\right)=0.65 \\\\\n",
    "P\\left(B_{1}\\right)=0.60, \\quad P\\left(B_{2}\\right)=0.30, \\quad P\\left(B_{3}\\right)=0.10\n",
    "\\end{gathered}\n",
    "$$\n",
    "最后由全概率公式知\n",
    "$$\n",
    "\\begin{aligned}\n",
    "P(A) &=P\\left(A \\mid B_{1}\\right) P\\left(B_{1}\\right)+P\\left(A \\mid B_{2}\\right) P\\left(B_{2}\\right)+P\\left(A \\mid B_{3}\\right) P\\left(B_{3}\\right) \\\\\n",
    "&=0.95 \\times 0.60+0.80 \\times 0.30+0.65 \\times 0.10 \\\\\n",
    "&=0.875\n",
    "\\end{aligned}\n",
    "$$\n",
    "这批产品的合格率为 $0.875$ 。\n",
    "\n",
    "（4）贝叶斯公式：\n",
    "\n",
    "结合条件概率公式、乘法公式和全概率公式，我们能得到强大的贝叶斯公式。现在，我们假定由于某些原因$P\\left(B_{k} \\mid A\\right)$直接计算是十分难求的，但是$P\\left(A \\mid B_{k}\\right)$求起来相对简单，但是我们需要求解$P\\left(B_{k} \\mid A\\right)$的值，怎么办呢？能不能用简单的$P\\left(A \\mid B_{k}\\right)$求解复杂的$P\\left(B_{k} \\mid A\\right)$呢？\n",
    "\n",
    "首先，我们写出所要求的复杂的$P\\left(B_{k} \\mid A\\right)$的定义公式，即：\n",
    "$$\n",
    "P\\left(B_{k} \\mid A\\right) = \\frac{P(AB_k)}{P(A)}\n",
    "$$\n",
    "其次，我们对分子分母分别使用乘法公式和全概率公式展开，即：\n",
    "$$\n",
    "P\\left(B_{k} \\mid A\\right)=\\frac{P\\left(A \\mid B_{k}\\right) P\\left(B_{k}\\right)}{\\sum_{i=1}^{n} P\\left(A \\mid B_{i}\\right) P\\left(B_{i}\\right)}, \\quad k=1,2, \\cdots, n\n",
    "$$\n",
    "至此，伟大的贝叶斯公式就被推导出来了。\n",
    "\n",
    "【例子】三门问题（Monty Hall problem ), 是一个源自博弈论的数学游戏问题, 大致出自美国的 电视游戏节目 Let's Make a Deal。问题的名字来自该节目的主持人蒙提・霍尔 (Monty Hall)。这个游戏的玩法是：参赛者会看见三扇关闭了的门，其中一扇的后面有一辆汽车，选中后面有车的那扇门就可以赢得该汽车, 而另外两扇门后面则各藏有一只山羊。当参赛者选定了一扇门，但未去开启它的时候，节目主持人会开启剩下两扇门的其中一扇, 露出其中一只山羊。主持人其后会问参赛者要不要换另一扇仍然关上的门。问题是：换另一扇门会否增加参赛者赢得汽车的机会率？\n",
    "\n",
    "解：\n",
    "   - 在主持人不打开门时, 选手抽中车的概率为 $1 / 3$ 。\n",
    "   - 假设：$\\mathrm{A}=$ 选手选择第一扇门，第一扇门中是车；$B=$ 选手选择第一扇门, 第二扇门中是车；$C=$ 选手选择第一扇门, 第三扇门口中是车； $\\mathrm{D}=$ 主持人打开第三扇门。即：\n",
    "   $$\n",
    "    \\begin{aligned}\n",
    "    &P(D \\mid A)=1 / 2 \\\\\n",
    "    &P(D \\mid B)=1 \\\\\n",
    "    &P(D \\mid C)=0 \\\\\n",
    "    &P(A)=P(B)=P(C)=1 / 3\\\\\n",
    "    &\\text{根据贝叶斯公式：}\\\\\n",
    "    &P(D)=P(A) P(D \\mid A)+P(B) P(D \\mid B)+P(C) P(D \\mid C)=1 / 2 \\\\\n",
    "    &P(A \\mid D)=P(A) P(D \\mid A) / P(D)=1 / 3 \\\\\n",
    "    &P(B \\mid D)=P(B) P(D \\mid B) / P(D)=2 / 3\n",
    "    \\end{aligned}\n",
    "    $$\n",
    "    \n",
    "下面，我们使用python代码模拟三门问题："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "a7ef0ade",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "换且能拿到车的概率：66.67 %\n",
      "不换也能拿到车的概率：33.33%\n"
     ]
    }
   ],
   "source": [
    "import random \n",
    "class MontyHall:\n",
    "    def __init__(self,n):\n",
    "        \"\"\"\n",
    "        n : int,试验的次数\n",
    "        \"\"\"\n",
    "        self.n = n\n",
    "        self.change = 0  # 记录换才能拿到车的次数\n",
    "        self.No_change = 0  # 记录不换才能拿到车的次数\n",
    "    def start(self):\n",
    "        for i in range(self.n):\n",
    "            door_list = [1,2,3]   ## 三扇门\n",
    "            challenger_door = random.choice(door_list)   ## 随机选择了其中一扇\n",
    "            car_door = random.choice(door_list)     ## 随机选定车的门\n",
    "            door_list.remove(challenger_door)   ## 没有被挑战者选中的剩下的门\n",
    "            if challenger_door == car_door:\n",
    "                host_door = random.choice(door_list)\n",
    "                door_list.remove(host_door)        # 不换才能拿车\n",
    "                self.No_change += 1\n",
    "            else:\n",
    "                self.change += 1      # 换了才能拿车\n",
    "        print(\"换且能拿到车的概率：%.2f \" % (self.change/self.n * 100) + \"%\")\n",
    "        print(\"不换也能拿到车的概率：%.2f\"% (self.No_change/self.n * 100) + \"%\")\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    mh = MontyHall(1000000)\n",
    "    mh.start()  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b839a0f1",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### 3. 一维随机变量及其分布函数和密度函数"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1999fb2",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "在刚才的讨论中，我们讨论了概率论中的一些基本概念，也着重介绍了条件概率及其衍生中的乘法公式以及全概率公式和贝叶斯公式。但是人们对随机现象的兴趣常常集中在其结果的某个数量方面。譬如,质量检验员在检查 20 个产品中关心的是不合格品的个数。若记 20 个产品中不合格品的个数为 $X$, 则这个 $X$ 可能取 $0,1,2, \\cdots, 20$ 中任一个数,可见此 $X$ 是变量。 至于这个 $X$ 取哪一个数要看检査结果,事先不能确定，故此 $X$ 的取值又带有随机性,这样的变量又称为随机变量。这个随机变量 $X$ 是质量检验员的注意点。有了随机变量后,有关事件的表示也方便了。如“ $X=2$ ”表示“ 20 个产品中 有 2 个不合格品”这一事件, 又如“ $X \\leqslant 2$ ”表示“ 20 个产品中有不多于 2 个不合格品”这一事件。随机变量 $X$ 是基本结果 $\\omega$ 的函数,即可把 $X$ 记为 $X(\\omega)$。假如一个随机变量仅取数轴上的有限个或可列个孤立点, 则称此随机变量为**离散随机变量**。值充满数轴上的一个区间 $(a, b)$ , 则称此随机变量为**连续随机变量**,其中 $a$ 可以是 $-\\infty$, $b$ 可以是$＋\\infty$。\n",
    "\n",
    "例如：\n",
    "   - 抛一枚硬币,正面出现次数 $X$ 是仅可能取 0 与 1 两个值的随机变量。 $X=0$ \"表示“出现反面”, $X=1$ 表示“出现正面”。类似地,检査一个产品,不合格的个数 $Y$ 也是一个仅能取 0 与 1 两个值的随机变量。 $Y=0$表示“合格品”, $Y=1$表示“不合格品”。\n",
    "   - 检査 $n$ 个产品, 不合格品数 $X$ 是可能取 $0,1, \\cdots, n$ 等 $n+1$ 个值的随机变量, “ $X=x$ \"表示“ $n$ 个产品中有 $x$ 个不合格品”。类似地, $n$ 台车床中需要维修的车床数 $Y$ 也是可能取 $0,1, \\cdots, n$ 等 $n+1$ 个值的随机变量, “ $Y=y$ ”表 “ $n$ 台车床中有 $y$ 台需要维修”。\n",
    "   - 测量误差 $X$ 是可在 $(-\\infty, \\infty)$ 上取值的随机变量。 “$|X| \\leqslant 1 $“ 表示“测量误差 $X$ 在 $[-1,+1]$ 内”。\n",
    "   - 电视机的寿命 $Y$ (单位: 小时) 是 $(0, \\infty)$ 上取值的随机变量, \" $Y>10000$ \"表示“电视机寿命超过一万小时”。类似地,小客车每公里的耗油量 $Y$ (单位:升)也可看作在 $(0, \\infty)$ 上取值的随机变量。 “$Y \\leqslant 0.5$ ”表示“小客车每公里的耗油量不超过半升。”\n",
    "\n",
    "现在，我们已经可以使用随机变量去表示随机事件，但是我们仍需考虑这个问题：随机变量 $X$ 取这些值的概率是多少?换句话说就是：随机事件对应的随机变量取这些值的概率是多少？计算一个由随机变量表示的随机事件的概率的思路有两种：**直接计算法（利用分布函数计算）** 和 **间接计算法（利用密度函数计算）**。\n",
    "\n",
    "接下来我们来一起学习下可以很方便计算随机变量的概率的函数：分布函数。（直接计算法）\n",
    "\n",
    "设 $X$ 为一个随机变量,对任意实数 $x$,事件“ $X \\leqslant x$ ”的概率 是 $x$ 的函数,记为\n",
    "$$\n",
    "F(x)=P(X \\leqslant x)\n",
    "$$\n",
    "这个函数称为 $X$ 的累积概率分布函数,简称分布函数。为什么要这么设置分布函数呢？原因可以从概率的本质入手，因为分布函数本身就是为了计算随机变量的概率。\n",
    "   - $ 0 \\leqslant F(x) \\leqslant 1$ 。 要记住,分布函数值是特定形式事件“ $X \\leqslant x$ ”的概率,而 概率总在 0 与 1 之间。\n",
    "   - $F(-\\infty)=\\lim _{x \\rightarrow-\\infty} F(x)=0$ ,这是因为事件“ $X \\leqslant-\\infty$ \"是不可能事件。\n",
    "   - $F(+\\infty)=\\lim _{x \\rightarrow+\\infty} F(x)=1$, 这是因为事件“ $X \\leqslant+\\infty$ \"是必然事件。 \n",
    "   - $F(x)$ 是非降函数, 即对任意 $x_{1}<x_{2}$, 有 $F\\left(x_{1}\\right) \\leqslant F\\left(x_{2}\\right)$ 。 这是因为事件 “$ X \\leqslant x_{2}$ ”包含事件\" $X \\leqslant x_{1} $\"。\n",
    "   \n",
    "因此：\n",
    "$$\n",
    "\\begin{aligned}\n",
    "&P(a<X \\leqslant b)=F(b)-F(a) \\\\\n",
    "&P(X=a)=F(a)-F(a-0) \\\\\n",
    "&P(X \\geqslant b)=1-F(b-0) \\\\\n",
    "&P(X>b)=1-F(b)\\\\\n",
    "&P(X<b)=F(b-0) \\\\\n",
    "&P(a<X<b)=F(b-0)-F(a) \\\\\n",
    "&P(a \\leqslant X \\leqslant b)=F(b)-F(a-0) \\\\\n",
    "&P(a \\leqslant X<b)=F(b-0)-F(a-0)\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "特别当 $F(x)$ 在 $a$ 与 $b$ 处连续时, 有\n",
    "$$\n",
    "F(a-0)=F(a), \\quad F(b-0)=F(b) \n",
    "$$\n",
    "\n",
    "例子：反正切函数$F(x)=\\frac{1}{\\pi}\\left(\\arctan x+\\frac{\\pi}{2}\\right),-\\infty<x<\\infty$是柯西分布的分布函数，函数如图所示：\n",
    "\n",
    "<div>\n",
    "<img src=\"./images/5.png\" width=\"400\" align=\"middle\"/>\n",
    "</div>\n",
    "\n",
    "若 $X$ 服从柯西分布, 则\n",
    "$$\n",
    "P(-1 \\leqslant X \\leqslant 1)=F(1)-F(-1)=\\frac{1}{\\pi}[\\arctan (1)-\\arctan (-1)]=\\frac{1}{\\pi}\\left[\\frac{\\pi}{4}-\\left(-\\frac{\\pi}{4}\\right)\\right]=\\frac{1}{2} \n",
    "$$\n",
    "\n",
    "分布函数是计算随机变量表示的随机事件的概率的直接方法，因为分布函数本身就是直接使用概率定义的。现在，我们来看看计算随机变量表示的随机事件的概率的间接方法——密度函数。先来学习连续型随机变量的密度函数，现在不直接假设随机变量的概率函数是什么，我们使用：某个区间内的概率 = 区间长度 * 长度内的概率密度，就好像一个小面积的质量等于面积内的密度 * 面积。因此，概率的计算变成以下的表示：对任意两个实数 $a$ 与 $b$,其中 $a<b$, 且 $a$ 可为 $-\\infty, b$ 可为 $+\\infty, X$ 在区间 $[a, b]$ 上取值的概率为曲线 $p(x)$ 在该区间上曲边梯形的面积,即\n",
    "$$\n",
    "P(a \\leqslant X \\leqslant b)=\\int_{a}^{b} p(x) d x\n",
    "$$\n",
    "则称密度函数 $p(x)$ 为连续随机变量 $X$ 的概率分布,或简称 $p(x)$ 为 $X$ 的密度 函数,记为 $X \\sim p(x)$, 读作“ $X$ 服从密度 $p(x)$ ”。\n",
    "\n",
    "由于概率密度函数$P(x)$表示的概率的密度，它应该遵守概率的基本特征（概率最大为1）：\n",
    "$$\n",
    "\\int_{-\\infty}^{\\infty} p(x) d x=1 ,\\;p(x) \\geqslant 0\n",
    "$$\n",
    "\n",
    "那与连续随机变量相对应的离散随机变量，它的“密度函数”怎么表示呢？对于离散随机变量来说，我们往往使用分布列去对应连续随机变量密度函数的概念。因为连续随机变量的密度函数使用的是积分来表达的，而离散情况下往往只需要简单的求和就可以了，实际上积分就是符号$\\int$就是拉长的求和符号$\\sum$他们本质上都是求和。因此，\n",
    "设 $X$ 是一个离散随机变量,如果 $X$ 的所有可能取值是 $x_{1}, x_{2}, \\cdots$, $x_{n}, \\cdots$, 则称 $X$ 取 $x_{i}$ 的概率\n",
    "$$\n",
    "p_{i}=p\\left(x_{i}\\right)=P\\left(X=x_{i}\\right), i=1,2, \\cdots, n, \\cdots\n",
    "$$\n",
    "为 $X$ 的概率分布列或简称为分布列, 记为 $X \\sim\\left\\{p_{i}\\right\\}$\n",
    "\n",
    "分布列如下图：\n",
    "$$\n",
    "\\begin{array}{c|ccccc}\n",
    "X & x_{1} & x_{2} & \\cdots & x_{n} & \\cdots \\\\\n",
    "\\hline P & p\\left(x_{1}\\right) & p\\left(x_{2}\\right) & \\cdots & p\\left(x_{n}\\right) & \\cdots\n",
    "\\end{array}\n",
    "$$\n",
    "\n",
    "例子：柯西分布的分布函数为：$F(x)=\\frac{1}{\\pi}\\left(\\arctan x+\\frac{\\pi}{2}\\right),-\\infty<x<\\infty$，求柯西分布的密度函数？\n",
    "解：\n",
    "$$\n",
    "F^{'}(x) = p(x)=\\frac{1}{\\pi} \\frac{1}{1+x^{2}}, \\quad-\\infty<x<\\infty \n",
    "$$\n",
    "\n",
    "例子：投掷一颗骰子，设$X$为投掷的点数，求随机变量$X$分布列和分布函数。\n",
    "\n",
    "解：\n",
    "\n",
    "分布列：\n",
    "$$\n",
    "\\begin{array}{c|cccccc}\n",
    "X & 1 & 2 & 3 & 4 & 5 & 6 \\\\\n",
    "\\hline P & \\frac{1}{6} & \\frac{1}{6} & \\frac{1}{6} & \\frac{1}{6} & \\frac{1}{6} & \\frac{1}{6}\n",
    "\\end{array}\n",
    "$$\n",
    "\n",
    "分布函数：\n",
    "$$\n",
    "F(x)=P(X \\leqslant x) = \\begin{cases}0, & x<1 \\\\ \\frac{i}{6}, & i \\le x < i+1, i=1,2,3,4,5 \\\\ 1, & x \\ge 6\\end{cases}\n",
    "$$\n",
    "\n",
    "【例子】如何使用python已知密度函数求分布函数/已知分布函数求密度函数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "4c9b5747",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\operatorname{atan}{\\left(x \\right)}}{\\pi} + \\frac{1}{2}$"
      ],
      "text/plain": [
       "atan(x)/pi + 1/2"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## 已知柯西分布的密度函数求分布函数\n",
    "from sympy import *\n",
    "x = symbols('x')\n",
    "p_x = 1/pi*(1/(1+x**2))\n",
    "integrate(p_x, (x, -oo, x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "2dd0ac12",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{1}{\\pi \\left(x^{2} + 1\\right)}$"
      ],
      "text/plain": [
       "1/(pi*(x**2 + 1))"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## 已知柯西分布的分布函数求密度函数\n",
    "from sympy import *\n",
    "x = symbols('x')\n",
    "f_x = 1/pi*(atan(x)+pi/2)\n",
    "diff(f_x,x,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a30589c",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "下面介绍常见的连续型随机变量及其密度函数：\n",
    "\n",
    "（1）均匀分布：\n",
    "\n",
    "一般地，在有限区间 $[a, b]$ 上为常数,在此区间外为零的密度函 数 $p(x)$ 都称为均匀分布,并记为 $U(a, b)$, 其密度函数为\n",
    "$$\n",
    "p(x)= \\begin{cases}\\frac{1}{b-a}, & a \\leqslant x \\leqslant b \\\\ 0, & \\text { 其它 }\\end{cases}\n",
    "$$\n",
    "均匀分布的分布函数为：\n",
    "$$\n",
    "F(x)= \\begin{cases}0, & x<a \\\\ \\frac{x-a}{b-a}, & a \\leqslant x<b \\\\ 1, & x \\geqslant b\\end{cases}\n",
    "$$\n",
    "均匀分布是最简单的，也是最常见的分布，例如：小明去约会，他下午14:00-18:00都**等可能**出现，那么出现的时间点就满足均匀分布。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "751ab016",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 【0，1】上的均匀分布\n",
    "a = float(0)\n",
    "b = float(1)\n",
    "\n",
    "x = np.linspace(a, b)\n",
    "y = np.full(shape = len(x),fill_value=1/(b - a))  # np.full 构造一个数组，用指定值填充其元素\n",
    "\n",
    "plt.plot(x,y,\"b\",linewidth=2)\n",
    "plt.ylim(0,1.2)\n",
    "plt.xlim(-1,2)\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('p (x)')\n",
    "plt.title('uniform distribution')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "974f6d81",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "（2）指数分布：\n",
    "\n",
    "若随机变量 $X$ 的密度函数为\n",
    "$$\n",
    "p(x)=\\left\\{\\begin{aligned}\n",
    "\\lambda e^{-\\lambda x}, & x \\geqslant 0 \\\\\n",
    "0, & x<0\n",
    "\\end{aligned}\\right.\n",
    "$$\n",
    "则称 $X$ 服从指数分布, 记作 $X \\sim \\operatorname{Exp}(\\lambda)$, 其中参数 $\\lambda>0$。其中 $\\lambda$ 是根据实际背景而定的正参数。假如某连续随机变量 $X \\sim \\operatorname{Exp}(\\lambda)$, 则表示 $X$ 仅可能取非负实数。\n",
    "\n",
    "指数分布的分布函数为：\n",
    "$$\n",
    "F(x)= \\begin{cases}1-\\mathrm{e}^{-\\lambda x}, & x \\geqslant 0 \\\\ 0, & x<0\\end{cases}\n",
    "$$\n",
    "实际中不少产品首次发生故障(需要维修)的时间服从指数分布。譬如,某种热水器首次发生故障的时间 $T$ (单位:小时)服从指数分布 $\\operatorname{Exp}(0.002)$, 即 $T$ 的密度函数为\n",
    "$$\n",
    "p(t)=\\left\\{\\begin{array}{cl}\n",
    "0.002 e^{-0.002 t}, & t \\geqslant 0 \\\\\n",
    "0, & t<0\n",
    "\\end{array}\\right.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "041c98dc",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 指数分布\n",
    "lam = float(1.5)\n",
    "\n",
    "x = np.linspace(0,15,100)\n",
    "y = lam * np.e**(-lam * x)\n",
    "\n",
    "plt.plot(x,y,\"b\",linewidth=2) \n",
    "plt.xlim(-5,10)\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('p (x)')\n",
    "plt.title('exponential distribution')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11af359e",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "（3）正态分布（高斯分布）\n",
    "\n",
    "正态分布是《概率论与数理统计》中最重要的一个分布，高斯 (Gauss, 1777-1855)在 研究误差理论时首先用正态分布来刻画误差的分布，所以正态分布又称为高斯分布。\n",
    "\n",
    "若随机变量 $X$ 的密度函数为\n",
    "$$\n",
    "p(x)=\\frac{1}{\\sqrt{2 \\pi} \\sigma} \\mathrm{e}^{-\\frac{(x-\\mu)^{2}}{2 \\sigma^{2}}}, \\quad-\\infty<x<\\infty,\n",
    "$$\n",
    "则称 $X$ 服从正态分布， 称 $X$ 为正态变量， 记作 $X \\sim N\\left(\\mu, \\sigma^{2}\\right)$。 其中参数 $-\\infty<\\mu<\\infty, \\sigma>0$。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "74996f40",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\sqrt{2} e^{- \\frac{\\mu^{2}}{2 \\sigma^{2}}} \\int\\limits_{-\\infty}^{x} e^{- \\frac{x^{2}}{2 \\sigma^{2}}} e^{\\frac{\\mu x}{\\sigma^{2}}}\\, dx}{2 \\sqrt{\\pi} \\sigma}$"
      ],
      "text/plain": [
       "sqrt(2)*exp(-mu**2/(2*sigma**2))*Integral(exp(-x**2/(2*sigma**2))*exp(mu*x/sigma**2), (x, -oo, x))/(2*sqrt(pi)*sigma)"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## 已知正态分布的密度函数求分布函数\n",
    "from sympy import *\n",
    "from sympy.abc import mu,sigma\n",
    "x = symbols('x')\n",
    "p_x = 1/(sqrt(2*pi)*sigma)*E**(-(x-mu)**2/(2*sigma**2))\n",
    "integrate(p_x, (x, -oo, x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "743974a3",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#正态分布\n",
    "import math\n",
    "mu = float(0)\n",
    "mu1 = float(2)\n",
    "sigma1 = float(1)\n",
    "sigma2 = float(1.25)*float(1.25)\n",
    "sigma3 = float(0.25)\n",
    "x = np.linspace(-5, 5, 1000)\n",
    "y1 = np.exp(-(x - mu)**2 / (2 * sigma1**2)) / (math.sqrt(2 * math.pi) * sigma1)\n",
    "y2 = np.exp(-(x - mu)**2 / (2 * sigma2**2)) / (math.sqrt(2 * math.pi) * sigma2)\n",
    "y3 = np.exp(-(x - mu)**2 / (2 * sigma3**2)) / (math.sqrt(2 * math.pi) * sigma3)\n",
    "y4 = np.exp(-(x - mu1)**2 / (2 * sigma1**2)) / (math.sqrt(2 * math.pi) * sigma1)\n",
    "plt.plot(x,y1,\"b\",linewidth=2,label=r'$\\mu=0,\\sigma=1$') \n",
    "plt.plot(x,y2,\"orange\",linewidth=2,label=r'$\\mu=0,\\sigma=1.25$') \n",
    "plt.plot(x,y3,\"yellow\",linewidth=2,label=r'$\\mu=0,\\sigma=0.5$') \n",
    "plt.plot(x,y4,\"b\",linewidth=2,label=r'$\\mu=2,\\sigma=1$',ls='--') \n",
    "plt.axvline(x=mu,ls='--')\n",
    "plt.text(x=0.05,y=0.5,s=r'$\\mu=0$')\n",
    "plt.axvline(x=mu1,ls='--')\n",
    "plt.text(x=2.05,y=0.5,s=r'$\\mu=2$')\n",
    "plt.xlim(-5,5)\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('p (x)')\n",
    "plt.title('normal distribution')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ff87f4f",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "- 如果固定 $\\sigma$， 改变 $\\mu$ 的值，则图形沿 $x$ 轴平移。也就是说正态密度函数的位置由参数 $\\mu$ 所确定， 因此亦称 $\\mu$ 为位置参数。\n",
    "- 如果固定 $\\mu$， 改变 $\\sigma$ 的值，则分布的位置不变,但 $\\sigma$ 愈小，曲线呈高而瘦，分布较为集中; $\\sigma$ 愈大，曲线呈矮而胖， 分布较为分散。也就是说正态密度函数的尺度由参数 $\\sigma$ 所确定， 因此称 $\\sigma$ 为尺度参数。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "562f419c",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 使用scipy计算pdf画图(非自定义函数)\n",
    "from scipy.stats import expon # 指数分布\n",
    "x = np.linspace(0.01,10,1000)  \n",
    "plt.plot(x, expon.pdf(x),'r-', lw=5, alpha=0.6, label='expon pdf')    # pdf表示求密度函数值\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"p (x)\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "c22fa99d",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 使用scipy计算cdf画图(非自定义函数)\n",
    "from scipy.stats import expon\n",
    "x = np.linspace(0.01,10,1000)  \n",
    "plt.plot(x, expon.cdf(x),'r-', lw=5, alpha=0.6, label='expon cdf')  # cdf表示求分布函数值\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"F (x)\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c98742cc",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "下面介绍常见的离散型随机变量及其分布列：\n",
    "\n",
    "（1）0-1分布（伯努利分布）：\n",
    "\n",
    "满足相互独立、只取两个值的随机变量通常称为伯努利（Bernoulli）随机变量。进行一次事件试验，该事件发生的概率为$p$，不发生的概率为$1-p$。这是一个最简单的分布，任何一个只有两种结果的随机现象都服从0-1分布。\n",
    "$$\n",
    "P\\{X=k\\}=p^{k}(1-p)^{1-k}\n",
    "$$\n",
    "其中 $k=0,1$ 。\n",
    "\n",
    "我们也可以写成分布列的表格形式：\n",
    "$$\n",
    "\\begin{array}{c|cccccc}\n",
    "X & 0 & 1  \\\\\n",
    "\\hline P & p & 1-p \n",
    "\\end{array}\n",
    "$$\n",
    "\n",
    "（2）二项分布：\n",
    "\n",
    "用 $B_{n, k}$ 表示事件“ $n$ 重伯努里试验中成功出现 $k$ 次”。如今我们用随机变量来表示这个事件。设 $X$ 为 $n$ 重伯努里试验中成功的次数,则有 $B_{n, k}=$ “$ X=k $” 。其中 $X$ 可能取的值为 $0,1, \\cdots, n$, 它取这些值的概率为\n",
    "$$\n",
    "P(X=x)=\\left(\\begin{array}{l}\n",
    "n \\\\\n",
    "x\n",
    "\\end{array}\\right) p^{x}(1-p)^{n-x}, \\quad x=0,1, \\cdots, n\n",
    "$$ \n",
    "\n",
    "例子：某特效药的临床有效率为 $0.95$， 今有 10 人服用， 问至少有 8 人治愈的概率是多少？\n",
    "\n",
    "解：解 设 $X$ 为 10 人中被治愈的人数， 则 $X \\sim b(10,0.95)$， 而所求概率为\n",
    "$$\n",
    "\\begin{aligned}\n",
    "P(X \\geqslant 8) &=P(X=8)+P(X=9)+P(X=10) \\\\\n",
    "&=\\left(\\begin{array}{c}\n",
    "10 \\\\\n",
    "8\n",
    "\\end{array}\\right) 0.95^{8} 0.05^{2}+\\left(\\begin{array}{c}\n",
    "10 \\\\\n",
    "9\n",
    "\\end{array}\\right) 0.95^{9} 0.05+\\left(\\begin{array}{c}\n",
    "10 \\\\\n",
    "10\n",
    "\\end{array}\\right) 0.95^{10} \\\\\n",
    "&=0.0746+0.3151+0.5987=0.9884 .\n",
    "\\end{aligned}\n",
    "$$\n",
    "10 人中至少有 8 人被治愈的概率为 $0.9884$。\n",
    "\n",
    "（3）泊松分布：\n",
    "\n",
    "泊松分布是 1837 年由法国数学家泊松 (Poisson, 1781-1840)首次提出的，泊松分布的分布列为：\n",
    "$$\n",
    "P(X=x)=\\frac{\\lambda^{x}}{x !} e^{-\\lambda}\n",
    "$$\n",
    "其中： $\\lambda>0$ 是常数，是区间事件发生率的均值。泊松分布是一种常用的离散分布, 它常与单位时间 (或单位面积、单位产品等)上 的计数过程相联系, 譬如,\n",
    "   - 在一天内，来到某商场的顾客数。（$\\lambda$就是单位时间内商场的顾客数）\n",
    "   - 在单位时间内，一电路受到外界电磁波的冲击次数。\n",
    "   - 1 平方米内， 玻璃上的气泡数。\n",
    "   - 一铸件上的砂眼数。\n",
    "   - 在一定时期内， 某种放射性物质放射出来的 $\\alpha$-粒子数， 等等。 \n",
    "\n",
    "以上的例子都服从泊松分布。 因此泊松分布的应用面是十分广泛的。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "e4a81e70",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 对比不同的lambda对泊松分布的影响\n",
    "import math\n",
    "# 构造泊松分布列的计算函数\n",
    "def poisson(lmd,x):\n",
    "    return pow(lmd,x)/math.factorial(x)*math.exp(-lmd)\n",
    "x = [i+1 for i in range(10)]\n",
    "lmd1 = 0.8\n",
    "lmd2 = 2.0\n",
    "lmd3 = 4.0\n",
    "lmd4 = 6.0\n",
    "p_lmd1 = [poisson(lmd1,i) for i in x]\n",
    "p_lmd2 = [poisson(lmd2,i) for i in x]\n",
    "p_lmd3 = [poisson(lmd3,i) for i in x]\n",
    "p_lmd4 = [poisson(lmd4,i) for i in x]\n",
    "\n",
    "plt.scatter(np.array(x), p_lmd1, c='b',alpha=0.7)\n",
    "plt.axvline(x=lmd1,ls='--')\n",
    "plt.text(x=lmd1+0.1,y=0.1,s=r\"$\\lambda=0.8$\")\n",
    "plt.ylim(-0.1,1)\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"p (x)\")\n",
    "plt.title(r\"$\\lambda = 0.8$\")\n",
    "plt.show()\n",
    "\n",
    "plt.scatter(np.array(x), p_lmd2, c='b',alpha=0.7)\n",
    "plt.axvline(x=lmd2,ls='--')\n",
    "plt.text(x=lmd2+0.1,y=0.1,s=r\"$\\lambda=2.0$\")\n",
    "plt.ylim(-0.1,1)\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"p (x)\")\n",
    "plt.title(r\"$\\lambda = 2.0$\")\n",
    "plt.show()\n",
    "\n",
    "plt.scatter(np.array(x), p_lmd3, c='b',alpha=0.7)\n",
    "plt.axvline(x=lmd3,ls='--')\n",
    "plt.text(x=lmd3+0.1,y=0.1,s=r\"$\\lambda=4.0$\")\n",
    "plt.ylim(-0.1,1)\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"p (x)\")\n",
    "plt.title(r\"$\\lambda = 4.0$\")\n",
    "plt.show()\n",
    "\n",
    "plt.scatter(np.array(x), p_lmd4, c='b',alpha=0.7)\n",
    "plt.axvline(x=lmd4,ls='--')\n",
    "plt.text(x=lmd4+0.1,y=0.1,s=r\"$\\lambda=6.0$\")\n",
    "plt.ylim(-0.1,1)\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"p (x)\")\n",
    "plt.title(r\"$\\lambda = 6.0$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16b46b12",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "从上图可以看出:\n",
    "   - 位于 $\\lambda$ （均值）附近概率较大.\n",
    "   - 随着 $\\lambda$ 的增加, 分布逐渐趋于对称."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "a44172d7",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 使用scipy的pmf和cdf画图\n",
    "from scipy.stats import binom\n",
    "n=10\n",
    "p = 0.5\n",
    "x=np.arange(1,n+1,1)\n",
    "pList=binom.pmf(x,n,p)\n",
    "plt.plot(x,pList,marker='o',alpha=0.7,linestyle='None')\n",
    "'''\n",
    "vlines用于绘制竖直线(vertical lines),\n",
    "参数说明：vline(x坐标值, y坐标最小值, y坐标值最大值)\n",
    "'''\n",
    "plt.vlines(x, 0, pList)\n",
    "plt.xlabel('随机变量：抛硬币10次')\n",
    "plt.ylabel('概率')\n",
    "plt.title('二项分布：n=%d,p=%0.2f' % (n,p))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70323253",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### 4. 一维随机变量的数字特征：期望、方差、分位数与中位数"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fece05f7",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "其实，在刚刚讨论的随机变量以及随机变量的密度函数、分布列等等概念，已经可以把随机事件描述的非常完整了，因为随机变量及其密度函数/分布列能把这个随机变量的所有信息都囊括起来。为什么需要随机变量的数字特征呢？因为在某些场合，我们不需要知道这个随机变量的方方面面，可能仅仅只需要知道某个侧面的信息。例如：我们知道明天的股票价格是一个随机变量，因为我们不知道明天股票的价格是多少。但是我们需要把明天的股票价格的每一个价格的概率都计算出来形成一个分布吗？显然不需要，我们更关心的是明天的股价在一般水平上比今天的股价是涨还是跌，如果涨了我们选择买入，跌了选择卖出。**因此，我们需要对随机变量的不同侧面进行描述，最好是能用一个数字去表述清楚而不是像分布一样是一个函数表达式，而这个数字就是我们所说的一维随机变量的数字特征。**\n",
    "\n",
    "（1）数学期望（均值）：\n",
    "\n",
    "“期望”在日常生活中常指有根据的希望,或发生可能性较大的希望。譬如，一位人寿保险经纪人告诉我们:“ 40 岁的妇女可期望再活 38 年。” 这不是说 40 岁的美国妇女都活到 78 岁,然后第二天立刻去世,而是指 40 岁的妇女中,有些可再活 20 年,有些再活 50 年,平均可再活 38 年,即再活 38 年 左右(如再活 $38 \\pm 10$ 年)的可能性大一些; 又如,“某种轮胎可期望行驶 6 万公里”,也是指此种轮胎平均可行驶 6 万公里,就个别轮胎来说,有的行驶可超过 6 万公里,有的行驶可能不到 6 万公里就报废,而行驶 6 万公里左右的可能性大一些。因此，下面谈及的“数学期望”是指用概率分布算得的一种加权平均。\n",
    "\n",
    "离散型随机变量的数学期望：\n",
    "\n",
    "设**离散随机变量** $X$ 的分布列为\n",
    "$$\n",
    "P=\\left(X=x_{i}\\right)=p\\left(x_{i}\\right), \\quad i=1,2, \\cdots, n\n",
    "$$\n",
    "则：\n",
    "$$\n",
    "E(X)=\\sum_{i=1}^{n} x_{i} p\\left(x_{i}\\right)\n",
    "$$\n",
    "\n",
    "连续型随机变量的数学期望：\n",
    "\n",
    "设**连续随机变量** $X$ 有密度函数 $p(x)$, 如果积分\n",
    "$$\n",
    "\\int_{-\\infty}^{\\infty}|x| p(x) d x\n",
    "$$\n",
    "有限,则称\n",
    "$$\n",
    "E(X)=\\int_{-\\infty}^{\\infty} x p(x) d x\n",
    "$$\n",
    "为 $X$ 的数学期望,简称期望,期望值或均值。如果积分无限,则说 $X$ 的数学期望不存在。\n",
    "\n",
    "数学期望的理论意义是深刻的, 它是消除随机性的主要手段！\n",
    "\n",
    "例子：以 $X$ 记一张彩票的奖金额，则 $X$ 的分布列如下：\n",
    "$$\n",
    "\\begin{array}{c|cccccccc}\n",
    "\\hline X & 500000 & 50000 & 5000 & 500 & 50 & 10 & 0 \\\\\n",
    "\\hline P & 0.000001 & 0.000009 & 0.00009 & 0.0009 & 0.009 & 0.09 & 0.9 & \\\\\n",
    "\\hline\n",
    "\\end{array}\n",
    "$$\n",
    "求一张彩票的平均所得奖金？\n",
    "\n",
    "解：\n",
    "$$\n",
    "E(X)=0.5+0.45+0.45+0.45+0.45+0.9+0=3.2\n",
    "$$\n",
    "\n",
    "假设每张福利彩票售价5元，每售出100万张就开一次奖，那么每一次开奖就会把筹得的500万中的320万（$3.2 \\times 1000000 = 3200000$）以奖金的形式返还给彩民，剩下的180万则用于福利事业和管理费用，这也是福利彩票的原理。\n",
    "\n",
    "例子：设 $X$ 服从区间 $(a, b)$ 上的均匀分布，求 $E(X)$。\n",
    "\n",
    "解：$X$ 的密度函数为：\n",
    "$$\n",
    "p(x)=\\left\\{\\begin{array}{cl}\n",
    "\\frac{1}{b-a}, & a<x<b, \\\\\n",
    "0, & \\text { 其他. }\n",
    "\\end{array}\\right.\n",
    "$$\n",
    "所以\n",
    "$$\n",
    "E(X)=\\int_{a}^{b} x \\cdot \\frac{1}{b-a} \\mathrm{~d} x=\\left.\\frac{1}{b-a} \\cdot \\frac{x^{2}}{2}\\right|_{a} ^{b}=\\frac{a+b}{2} .\n",
    "$$\n",
    "这个结果是可以理解的，因为 $X$ 在区间 $(a, b)$ 上的取值是均匀的，所以它的平均取值当然应该是 $(a, b)$ 的 “中点”, 即 $(a+b) / 2$。\n",
    "\n",
    "数学期望的性质：\n",
    "   - 若 $c$ 是常数， 则 $E(c)=c$。\n",
    "   - 对任意常数 $a$， 有$E(a X)=a E(X)$。\n",
    "   - 设 $(X, Y)$ 是二维随机变量, 则有$E(X+Y)=E(X)+E(Y)$\n",
    "   - **若随机变量 $X$ 与 $Y$ 相互独立**, 则有$E(X Y)=E(X) E(Y) $\n",
    "   \n",
    "\n",
    "**下面给出常见的分布的数学期望：**\n",
    "   - 0-1分布：$E(X)=p$\n",
    "   - 二项分布：$E(X) = np$\n",
    "   - 泊松分布：$E(X) = \\lambda$\n",
    "   - 均匀分布：$E(X) = \\frac{a+b}{2}$\n",
    "   - 指数分布：$E(X) = \\frac{1}{\\lambda}$\n",
    "   - 正态分布：$E(X) = \\mu$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c2f740c",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "（2）方差与标准差：\n",
    "\n",
    "随机变量 $X$ 的数学期望 $E(X)$ 是分布的一种**位置特征数**， 它刻画了 $X$ 的取值总在 $E(X)$ 周围波动。但这个位置特征数无法反映出随机变量取值的“波动大小”，譬如 $X$ 与 $Y$ 的分布列分别为：\n",
    "$$\n",
    "\\begin{array}{c|ccc}\n",
    "X & -1 & 0 & 1 \\\\\n",
    "\\hline P & 1 / 3 & 1 / 3 & 1 / 3\n",
    "\\end{array}\n",
    "$$\n",
    "与\n",
    "$$\n",
    "\\begin{array}{c|ccc}\n",
    "Y & -10 & 0 & 10 \\\\\n",
    "\\hline P & 1 / 3 & 1 / 3 & 1 / 3\n",
    "\\end{array}\n",
    "$$\n",
    "尽管它们的数学期望都是 0 ， 但显然 $Y$ 取值的波动要比 $X$ 取值的波动大。 如何用数值来 反映随机变量取值的“波动”大小，方差与标准差是一个不错的衡量指标。\n",
    "\n",
    "方差在金融中扮演着重要的作用，就拿刚刚的明天的股票价格这个随机变量来说，如果明天的股价波动较大，往往代表着明天的股价不稳定程度高，风险大，即使明天的股价期望比今天要高，也不会选择买入股票，因为很有可能股价会比今天低而导致损失。因此，方差是衡量随机变量波动程度的数学量，具体的：数学期望 $E(X)$ 是分布的位置特征数，它总位于分布的中心，随机变量 $X$ 的取值总在其周围波动。方差是度量此种波动大小的最重要的特征数。\n",
    "\n",
    "\n",
    "若随机变量 $X^{2}$ 的数学期望 $E\\left(X^{2}\\right)$ 存在， 则称偏差平方 $(X-E(X))^{2}$ 的数学期望 $E(X-E(X))^{2}$ 为随机变量 $X$ (或相应分布) 的方差， 记为：\n",
    "$$\n",
    "\\operatorname{Var}(X)=E(X-E(X))^{2}\n",
    "$$\n",
    "\n",
    "离散型随机变量的方差：\n",
    "$$\n",
    "\\sum_{i}\\left(x_{i}-E(X)\\right)^{2} p\\left(x_{i}\\right)\n",
    "$$\n",
    "连续型随机变量的方差：\n",
    "$$\n",
    "\\int_{-\\infty}^{\\infty}(x-E(X))^{2} p(x) \\mathrm{d} x\n",
    "$$\n",
    "方差的正平方根 $[\\operatorname{Var}(X)]^{1 / 2}$ 称为随机变量 $X($ 或相应分布 $)$ 的标准差,记为 $\\sigma_{X}$ 或 $\\sigma(X)$ 。\n",
    "\n",
    "例子：某人有一笔资金， 可投人两个项目： 房地产和商业, 其收益都与市场状态有关。 若把末来市场划分为好、中、差三个等级， 其发生的概率分别为 $0.2 、 0.7 、 0.1$。 通过调查，该投资者认为投资于房地产的收益 $X$ (万元) 和投资于商业的收益 $Y($ 万元) 的分布分别为：\n",
    "$$\n",
    "\\begin{array}{c|ccc}\n",
    "X & 11 & 3 & -3 \\\\\n",
    "\\hline P & 0.2 & 0.7 & 0.1\n",
    "\\end{array}\n",
    "$$\n",
    "与\n",
    "$$\n",
    "\\begin{array}{c|ccc}\n",
    "Y & 6 & 4 & -1 \\\\\n",
    "\\hline P & 0.2 & 0.7 & 0.1\n",
    "\\end{array}\n",
    "$$\n",
    "解：先来看看平均收益（数学期望）：\n",
    "$$\n",
    "\\begin{aligned}\n",
    "&E(X)=11 \\times 0.2+3 \\times 0.7+(-3) \\times 0.1=4.0 \\text { (万元 }) \\\\\n",
    "&E(Y)=6 \\times 0.2+4 \\times 0.7+(-1) \\times 0.1=3.9(\\text { 万元 }) \n",
    "\\end{aligned}\n",
    "$$\n",
    "显然，投资房地产的收益比投资商业的收益大，大约平均大0.1万元。下面来计算各自投资的风险（方差/标准差）：\n",
    "\n",
    "方差：\n",
    "$$\n",
    "\\begin{gathered}\n",
    "\\operatorname{Var}(X)=(11-4)^{2} \\times 0.2+(3-4)^{2} \\times 0.7+(-3-4)^{2} \\times 0.1=15.4 \\\\\n",
    "\\operatorname{Var}(Y)=(6-3.9)^{2} \\times 0.2+(4-3.9)^{2} \\times 0.7+(-1-3.9)^{2} \\times 0.1=3.29\n",
    "\\end{gathered}\n",
    "$$\n",
    "标准差：\n",
    "$$\n",
    "\\sigma(X)=\\sqrt{15.4}=3.92, \\sigma(Y)=\\sqrt{3.29}=1.81\n",
    "$$\n",
    "由于标准差越大，说明投资的收益波动越大，那么风险也就越大。虽然投资房地产的平均收益比投资商业的平均收益大0.1万元，但是前者风险却是后者的两倍大，如果综合衡量收益与风险，还是投资商业为妙。\n",
    "\n",
    "方差的性质：\n",
    "   - 最重要的性质：$\\operatorname{Var}(X)=E\\left(X^{2}\\right)-[E(X)]^{2}$\n",
    "   - 常数的方差为 0 ， 即 $\\operatorname{Var}(c)=0$， 其中 $c$ 是常数。\n",
    "   - 若 $a, b$ 是常数，则 $\\operatorname{Var}(a X+b)=a^{2} \\operatorname{Var}(X)$。\n",
    "   - 若随机变量 $X$ 与 $Y$ 相互独立， 则有$\\operatorname{Var}(X \\pm Y)=\\operatorname{Var}(X)+\\operatorname{Var}(Y) $\n",
    "\n",
    "常见分布的方差：\n",
    "   - 0-1分布：$Var(X) = p(1-p)$\n",
    "   - 二项分布：$Var(X) = np(1-p)$\n",
    "   - 泊松分布：$Var(X) = \\lambda$\n",
    "   - 均匀分布：$Var(X) = \\frac{(b-a)^{2}}{12}$\n",
    "   - 正态分布：$Var(X) = \\sigma^2$\n",
    "   - 指数分布：$Var(X) = \\frac{1}{\\lambda^{2}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "6957ca8d",
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0-1分布的数字特征：均值:0.5；方差:0.25；标准差:0.5\n",
      "二项分布b(100,0.5)的数字特征：均值:50.0；方差:25.0；标准差:5.0\n",
      "泊松分布P(0.6)的数字特征：均值:0.6；方差:0.6；标准差:0.7745966692414834\n",
      "特定离散随机变量的数字特征：均值:3.5；方差:2.916666666666666；标准差:1.707825127659933\n",
      "均匀分布U(1,1+5)的数字特征：均值:3.5；方差:2.083333333333333；标准差:1.4433756729740643\n",
      "正态分布N(0,0.0001)的数字特征：均值:0.0；方差:0.0001；标准差:0.01\n",
      "指数分布Exp(5)的数字特征：均值:0.2；方差:0.04000000000000001；标准差:0.2\n",
      "标准正态分布的数字特征：均值:-6.963277549967673e-16；方差:0.9999999993070242；标准差:0.999999999653512\n",
      "Exp(5.0)分布的数字特征：均值:0.20826187507584426；方差:0.03678414422845682；标准差:0.19179192951857182\n",
      "dist分布的数字特征：均值:3.333333333333333；方差:1.388888888888891；标准差:1.1785113019775801\n"
     ]
    }
   ],
   "source": [
    "# 使用scipy计算常见分布的均值与方差：(如果忘记公式的话直接查，不需要查书了)\n",
    "from scipy.stats import bernoulli   # 0-1分布\n",
    "from scipy.stats import binom   # 二项分布\n",
    "from scipy.stats import poisson  # 泊松分布\n",
    "from scipy.stats import rv_discrete # 自定义离散随机变量\n",
    "from scipy.stats import uniform # 均匀分布\n",
    "from scipy.stats import expon # 指数分布\n",
    "from scipy.stats import norm # 正态分布\n",
    "from scipy.stats import rv_continuous  # 自定义连续随机变量\n",
    "\n",
    "print(\"0-1分布的数字特征：均值:{}；方差:{}；标准差:{}\".format(bernoulli(p=0.5).mean(), \n",
    "                                  bernoulli(p=0.5).var(), \n",
    "                                  bernoulli(p=0.5).std()))\n",
    "print(\"二项分布b(100,0.5)的数字特征：均值:{}；方差:{}；标准差:{}\".format(binom(n=100,p=0.5).mean(), \n",
    "                                  binom(n=100,p=0.5).var(), \n",
    "                                  binom(n=100,p=0.5).std()))\n",
    "## 模拟抛骰子的特定分布\n",
    "xk = np.arange(6)+1\n",
    "pk = np.array([1.0/6]*6)\n",
    "print(\"泊松分布P(0.6)的数字特征：均值:{}；方差:{}；标准差:{}\".format(poisson(0.6).mean(), \n",
    "                                  poisson(0.6).var(), \n",
    "                                  poisson(0.6).std()))\n",
    "print(\"特定离散随机变量的数字特征：均值:{}；方差:{}；标准差:{}\".format(rv_discrete(name='dice', values=(xk, pk)).mean(), \n",
    "                                  rv_discrete(name='dice', values=(xk, pk)).var(), \n",
    "                                  rv_discrete(name='dice', values=(xk, pk)).std()))\n",
    "print(\"均匀分布U(1,1+5)的数字特征：均值:{}；方差:{}；标准差:{}\".format(uniform(loc=1,scale=5).mean(), \n",
    "                                  uniform(loc=1,scale=5).var(), \n",
    "                                  uniform(loc=1,scale=5).std()))\n",
    "print(\"正态分布N(0,0.0001)的数字特征：均值:{}；方差:{}；标准差:{}\".format(norm(loc=0,scale=0.01).mean(), \n",
    "                                  norm(loc=0,scale=0.01).var(), \n",
    "                                  norm(loc=0,scale=0.01).std()))\n",
    "\n",
    "lmd = 5.0  # 指数分布的lambda = 5.0\n",
    "print(\"指数分布Exp(5)的数字特征：均值:{}；方差:{}；标准差:{}\".format(expon(scale=1.0/lmd).mean(), \n",
    "                                  expon(scale=1.0/lmd).var(), \n",
    "                                  expon(scale=1.0/lmd).std()))\n",
    "\n",
    "## 自定义标准正态分布\n",
    "class gaussian_gen(rv_continuous):\n",
    "    def _pdf(self, x): # tongguo \n",
    "        return np.exp(-x**2 / 2.) / np.sqrt(2.0 * np.pi)\n",
    "gaussian = gaussian_gen(name='gaussian')\n",
    "print(\"标准正态分布的数字特征：均值:{}；方差:{}；标准差:{}\".format(gaussian().mean(), \n",
    "                                  gaussian().var(), \n",
    "                                  gaussian().std()))\n",
    "\n",
    "## 自定义指数分布\n",
    "import math\n",
    "class Exp_gen(rv_continuous):\n",
    "    def _pdf(self, x,lmd):\n",
    "        y=0\n",
    "        if x>0:\n",
    "            y = lmd * math.e**(-lmd*x)\n",
    "        return y\n",
    "Exp = Exp_gen(name='Exp(5.0)')\n",
    "print(\"Exp(5.0)分布的数字特征：均值:{}；方差:{}；标准差:{}\".format(Exp(5.0).mean(), \n",
    "                                  Exp(5.0).var(), \n",
    "                                  Exp(5.0).std()))\n",
    "\n",
    "## 通过分布函数自定义分布\n",
    "class Distance_circle(rv_continuous):                 #自定义分布xdist\n",
    "    \"\"\"\n",
    "    向半径为r的圆内投掷一点，点到圆心距离的随机变量X的分布函数为:\n",
    "    if x<0: F(x) = 0;\n",
    "    if 0<=x<=r: F(x) = x^2 / r^2\n",
    "    if x>r: F(x)=1\n",
    "    \"\"\"\n",
    "    def _cdf(self, x, r):                   #累积分布函数定义随机变量\n",
    "        f=np.zeros(x.size)                  #函数值初始化为0\n",
    "        index=np.where((x>=0)&(x<=r))           #0<=x<=r\n",
    "        f[index]=((x[index])/r[index])**2       #0<=x<=r\n",
    "        index=np.where(x>r)                     #x>r\n",
    "        f[index]=1                              #x>r\n",
    "        return f\n",
    "dist = Distance_circle(name=\"distance_circle\")\n",
    "print(\"dist分布的数字特征：均值:{}；方差:{}；标准差:{}\".format(dist(5.0).mean(), \n",
    "                                  dist(5.0).var(), \n",
    "                                  dist(5.0).std()))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6dff7506",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "（3）分位数与中位数：\n",
    "\n",
    "一般来说，分位数和中位数的讨论往往是基于连续型随机变量来说的，因为离散型随机变量的某个概率对应的分位数和中位数有可能不唯一或者不存在。那么什么是分位数呢？分位数和数学期望一样，都是描述随机变量的位置的数字特征，我们把累计概率等于p所对应的随机变量取值x为p分位数，具体是：\n",
    "\n",
    "设连续随机变量 $X$ 的分布函数为 $F(x)$，密度函数为 $p(x)$。 对任意 $p \\in(0,1)$， 称满足条件\n",
    "$$\n",
    "F\\left(x_{p}\\right)=\\int_{-\\infty}^{x_{p}} p(x) \\mathrm{d} x=p\n",
    "$$\n",
    "的 $x_{p}$ 为此分布的 $p$ 分位数， 又称下侧 $p$ 分位数。\n",
    "\n",
    "<div>\n",
    "<img src=\"./images/6.png\" width=\"400\" align=\"middle\"/>\n",
    "</div>\n",
    "\n",
    "分位数与上侧分位数是可以相互转换的， 其转换公式如下：\n",
    "$$\n",
    "x_{p}^{\\prime}=x_{1-p}, \\quad x_{p}=x_{1-p}^{\\prime} \n",
    "$$\n",
    "\n",
    "**中位数就是p=0.5时的分位数点**，具体为：\n",
    "\n",
    "设连续随机变量 $X$ 的分布函数为 $F(x)$， 密度函数为 $p(x)$。 称 $p=0.5$ 时的 $p$ 分位数 $x_{0.5}$ 为此分布的中位数，即 $x_{0.5}$ 满足\n",
    "$$\n",
    "F\\left(x_{0.5}\\right)=\\int_{-\\infty}^{x_{0.5}} p(x) \\mathrm{d} x=0.5 \n",
    "$$\n",
    "\n",
    "<div>\n",
    "<img src=\"./images/7.png\" width=\"400\" align=\"middle\"/>\n",
    "</div>\n",
    "\n",
    "数学期望与中位数都是属于位置特征数，但是有时候中位数可能比期望更能说明问题。假如某个城市的平均薪资为5000，中位数薪资为4000，那么能说明有一半的人收入少于4000而有一般大于等于4000。但是平均薪资却有5000，说明了有相当一部分的高收入人群拉高了收入均数，该城市的薪资差异较大。一般来说，均值与中位数相差不大往往能代表系统的结构是正常的，如果偏离较大，则说明系统内结构出现了偏离。中位数往往比均值更加稳健，因为不容易受到极端数据的影响，但是中位数计算比较麻烦，接受起来也比较麻烦；均值会受到极端数据的影响，但是计算简单，也容易接受。\n",
    "\n",
    "【例子】使用python计算标准正态分布的0.25，0.5（中位数），0.75，0.95分位数点。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "780d2fdb",
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "标准正态分布的0.25分位数： -0.6744897501960817\n",
      "标准正态分布的0.5分位数： 0.0\n",
      "标准正态分布的0.75分位数： 0.6744897501960817\n",
      "标准正态分布的0.95分位数： 1.6448536269514722\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "print(\"标准正态分布的0.25分位数：\",norm(loc=0,scale=1).ppf(0.25))   # 使用ppf计算分位数点\n",
    "print(\"标准正态分布的0.5分位数：\",norm(loc=0,scale=1).ppf(0.5))\n",
    "print(\"标准正态分布的0.75分位数：\",norm(loc=0,scale=1).ppf(0.75))\n",
    "print(\"标准正态分布的0.95分位数：\",norm(loc=0,scale=1).ppf(0.95))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32da3418",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### 5. 多维随机变量及其联合分布、边际分布、条件分布"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d407779",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "在之前关于随机变量的讨论中，我们仅仅只研究了单一随机变量及其分布情况，但是现实中的问题往往影响的因素有很多而且是相互影响的。例如：人的身高与什么因素相关？可能与每天吃钙物质的量、影响身高基因的数量、基因的表达情况等等。单一影响因素并不能满足日常问题的研究，因此需要引入多维随机变量的概念。通俗的说，多维随机变量就是多个随机变量的结合，从一个推广到多个，在线性代数中我们已经干过这件事，那就是使用向量去表达！具体地说：\n",
    "\n",
    "若随机变量 $X_{1}(\\omega), X_{2}(\\omega), \\cdots, X_{n}(\\omega)$ 定义在同一个基本空间 $\\Omega=\\{\\omega\\}$ 上， 则称\n",
    "$$\n",
    "\\boldsymbol{X}(\\omega)=\\left(X_{1}(\\omega), X_{2}(\\omega), \\cdots, X_{n}(\\omega)\\right)\n",
    "$$ \n",
    "是一个多维随机变量，也称为n维随机向量。\n",
    "\n",
    "（1.1）n维随机变量的联合分布函数：\n",
    "\n",
    "一维随机变量的分布函数是一个关于x的函数，而n维随机变量的联合分布函数就是关于n个自变量的函数：\n",
    "\n",
    "设 $X=\\left(X_{1}, X_{2}, \\cdots, X_{n}\\right)$ 是 $n$ 维随机变量， 对任意 $n$ 个实数 $x_{1}, x_{2}, \\cdots, x_{n}$ 所组成的 $n$ 个事件 $X_{1} \\leqslant x_{1},X_{2} \\leqslant x_{2} , \\cdots, X_{n} \\leqslant x_{n} $ 同时发生的概率\n",
    "$$\n",
    "F\\left(x_{1}, x_{2}, \\cdots, x_{n}\\right)=P\\left(X_{1} \\leqslant x_{1}, X_{2} \\leqslant x_{2}, \\cdots, X_{n} \\leqslant x_{n}\\right)\n",
    "$$\n",
    "称为 $n$ 维随机变量 $\\boldsymbol{X}$ 的联合分布函数。\n",
    "\n",
    "（1.2）多维连续随机变量的联合密度函数：\n",
    "\n",
    "一维随机变量的密度函数是通过分布函数来确定的，也就是分布函数是密度函数的积分，那推广至多维随机变量也是如此：\n",
    "\n",
    "设二维随机变量 $(X, Y)$ 的分布函数为 $F(x, y)$ 。假如各分量 $X$ 和 $Y$ 都是一维连续随机变量，并存在定义在平面上的非负函数 $p(x, y)$，使得\n",
    "$$\n",
    "F(x, y)=\\int_{-\\infty}^{x} \\int_{-\\infty}^{y} p(x, y) d x d y\n",
    "$$\n",
    "则称 $(X, Y)$ 为二维连续随机变量，$p(x, y)$ 称为 $(X, Y)$ 的联合概率密度函数， 或简称联合密度。\n",
    "\n",
    "在 $F(x, y)$ 偏导数存在的点上有\n",
    "$$\n",
    "p(x, y)=\\frac{\\partial^{2}}{\\partial x \\partial y} F(x, y) \n",
    "$$\n",
    "\n",
    "（1.3）多维离散随机变量的联合分布列：\n",
    "\n",
    "如果二维随机变量 $(X, Y)$ 只取有限个或可列个数对 $\\left(x_{i}, y_{j}\\right)$， 则称 $(X, Y)$ 为二维离散随机变量， 称\n",
    "$$\n",
    "p_{i j}=P\\left(X=x_{i}, Y=y_{j}\\right), \\quad i, j=1,2, \\cdots\n",
    "$$\n",
    "为 $(X, Y)$ 的联合分布列， 也可用如下表格形式记联合分布列：\n",
    "<div>\n",
    "<img src=\"./images/8.png\" width=\"600\" align=\"middle\"/>\n",
    "</div>\n",
    "\n",
    "例子：从 $1,2,3,4$ 中任取一数记为 $X$， 再从 $1,2, \\cdots, X$ 中任取一数记为 $Y$。 求 $(X, Y)$ 的联合分布列及 $P(X=Y)$。\n",
    "\n",
    "解：\n",
    "\n",
    "<div>\n",
    "<img src=\"./images/9.png\" width=\"600\" align=\"middle\"/>\n",
    "</div>\n",
    "\n",
    "$$\n",
    "P(X=Y)=p_{11}+p_{22}+p_{33}+p_{44}=\\frac{1}{4}+\\frac{1}{8}+\\frac{1}{12}+\\frac{1}{16}=\\frac{25}{48}=0.5208\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "11b8f0c8",
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 绘制二维正态分布的联合概率密度曲面图\n",
    "from scipy.stats import multivariate_normal\n",
    "from mpl_toolkits.mplot3d import axes3d\n",
    "x, y = np.mgrid[-5:5:.01, -5:5:.01]  # 返回多维结构\n",
    "pos = np.dstack((x, y))\n",
    "rv = multivariate_normal([0.5, -0.2], [[2.0, 0.3], [0.3, 0.5]])\n",
    "z = rv.pdf(pos)\n",
    "plt.figure('Surface', facecolor='lightgray',figsize=(12,8))\n",
    "ax = plt.axes(projection='3d')\n",
    "ax.set_xlabel('X', fontsize=14)\n",
    "ax.set_ylabel('Y', fontsize=14)\n",
    "ax.set_zlabel('P (X,Y)', fontsize=14)\n",
    "ax.plot_surface(x, y, z, rstride=50, cstride=50, cmap='jet')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "a2d3c691",
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 绘制二维正态分布的联合概率密度等高线图\n",
    "from scipy.stats import multivariate_normal\n",
    "x, y = np.mgrid[-1:1:.01, -1:1:.01]\n",
    "pos = np.dstack((x, y))\n",
    "rv = multivariate_normal([0.5, -0.2], [[2.0, 0.3], [0.3, 0.5]])\n",
    "z = rv.pdf(pos)\n",
    "fig = plt.figure(figsize=(8,6))\n",
    "ax2 = fig.add_subplot(111)\n",
    "ax2.set_xlabel('X', fontsize=14)\n",
    "ax2.set_ylabel('Y', fontsize=14)\n",
    "ax2.contourf(x, y, z, rstride=50, cstride=50, cmap='jet')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16c52c8d",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "（2.1）边际分布函数：\n",
    "\n",
    "多维随机变量的联合密度函数、联合分布列或者联合分布函数蕴含了这个多维随机向量的所有信息，这些信息主要包括：\n",
    "   - 每个分量的分布 (每个分量的所有信息), 即边际分布。\n",
    "   - 两个分量之间的关联程度， 用协方差和相关系数来描述。 （后面介绍）\n",
    "   - 给定一个分量时，另一个分量的分布, 即条件分布。\n",
    "\n",
    "多维随机向量中，每个元素即单一随机变量都可能受到这组向量其他随机变量的影响，这种影响可以通过协方差来反映。所谓的边际分布，就是指多维随机向量中的其中一个随机变量$X$排除其他随机变量影响的分布，即$X$自身的分布。具体来说就是：\n",
    "\n",
    "如果在二维随机变量 $(X, Y)$ 的联合分布函数 $F(x, y)$ 中令 $y \\rightarrow \\infty$， 由于 $\\{Y<\\infty\\}$ 为必然事件， 故可得\n",
    "$$\n",
    "\\lim _{y \\rightarrow \\infty} F(x, y)=P(X \\leqslant x, Y<\\infty)=P(X \\leqslant x),\n",
    "$$\n",
    "这是由 $(X, Y)$ 的联合分布函数 $F(x, y)$ 求得的 $X$ 的分布函数， 被称为 $X$ 的边际分布, 记为\n",
    "$$\n",
    "F_{X}(x)=F(x, \\infty)\n",
    "$$\n",
    "类似地， 在 $F(x, y)$ 中令 $x \\rightarrow \\infty$， 可得 $Y$ 的边际分布\n",
    "$$\n",
    "F_{Y}(y)=F(\\infty, y) \n",
    "$$\n",
    "\n",
    "例子：设二维随机变量 $(X, Y)$ 的联合分布函数为\n",
    "$$\n",
    "F(x, y)= \\begin{cases}1-\\mathrm{e}^{-x}-\\mathrm{e}^{-y}+\\mathrm{e}^{-x-y-\\lambda x y}, & x>0, y>0 . \\\\ 0, & \\text { 其他. }\\end{cases}\n",
    "$$\n",
    "这个分布被称为二维指数分布，其中参数 $\\lambda>0$。\n",
    "\n",
    "解：\n",
    "$$\n",
    "\\begin{aligned}\n",
    "&F_{X}(x)=F(x, \\infty)= \\begin{cases}1-\\mathrm{e}^{-x}, & x>0, \\\\\n",
    "0, & x \\leqslant 0 .\\end{cases} \\\\\n",
    "&F_{Y}(y)=F(\\infty, y)= \\begin{cases}1-\\mathrm{e}^{-y}, & y>0, \\\\\n",
    "0, & y \\leqslant 0 .\\end{cases}\n",
    "\\end{aligned}\n",
    "$$\n",
    "它们都是一维指数分布。不同的 $\\lambda>0$ 对应不同的二维指数分布， 但它们的两个边际分布与参数 $\\lambda>0$ 无关。 这说明：二维联合分布不仅含有每个分量的概率分布， 而且还含有 两个变量 $X$ 与 $Y$ 间关系的信息。\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c5b4132",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "（2.2）边际密度函数：\n",
    "\n",
    "如果二维连续随机变量 $(X, Y)$ 的联合密度函数为 $p(x, y)$， 因为\n",
    "$$\n",
    "\\begin{aligned}\n",
    "&F_{X}(x)=F(x, \\infty)=\\int_{-\\infty}^{x}\\left(\\int_{-\\infty}^{\\infty} p(u, v) \\mathrm{d} v\\right) \\mathrm{d} u=\\int_{-\\infty}^{x} p_{X}(u) \\mathrm{d} u \\\\\n",
    "&F_{Y}(y)=F(\\infty, y)=\\int_{-\\infty}^{y}\\left(\\int_{-\\infty}^{\\infty} p(u, v) \\mathrm{d} u\\right) \\mathrm{d} v=\\int_{-\\infty}^{y} p_{Y}(v) \\mathrm{d} v\n",
    "\\end{aligned}\n",
    "$$\n",
    "其中 $p_{X}(x)$ 和 $p_{Y}(y)$ 分别为\n",
    "$$\n",
    "\\begin{aligned}\n",
    "&p_{X}(x)=\\int_{-\\infty}^{\\infty} p(x, y) \\mathrm{d} y \\\\\n",
    "&p_{Y}(y)=\\int_{-\\infty}^{\\infty} p(x, y) \\mathrm{d} x\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "【例子】设二维随机变量 $(X, Y)$ 的联合密度函数为\n",
    "$$\n",
    "p(x, y)= \\begin{cases}1, & 0<x<1,|y|<x, \\\\ 0, & \\text { 其他. }\\end{cases}\n",
    "$$\n",
    "试求: 边际密度函数 $p_{X}(x)$ 和 $p_{Y}(y)$。\n",
    "$$\n",
    "p_{x}(x)= \\begin{cases}2 x, & 0<x<1, \\\\ 0, & \\text { 其他. }\\end{cases}\n",
    "$$\n",
    "与\n",
    "$$\n",
    "p_{Y}(y)= \\begin{cases}1+y, & -1<y<0, \\\\ 1-y, & 0<y<1, \\\\ 0, & \\text { 其他. }\\end{cases}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "d401dcd2",
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\begin{cases} x + \\max\\left(- x, x\\right) & \\text{for}\\: x > 0 \\wedge x < 1 \\\\0 & \\text{otherwise} \\end{cases}$"
      ],
      "text/plain": [
       "Piecewise((x + Max(-x, x), (x > 0) & (x < 1)), (0, True))"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 求边际密度函数 p_{X}(x)\n",
    "from sympy import *\n",
    "x = symbols('x')\n",
    "y = symbols('y')\n",
    "p_xy = Piecewise((1,And(x>0,x<1,y<x,y>-x)),(0,True))\n",
    "integrate(p_xy, (y, -oo, oo))   ## 由于0<x<1时候，那么x>-x，即2x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "ed94f431",
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\max\\left(0, - y, y\\right) + \\max\\left(1, - y, y\\right)$"
      ],
      "text/plain": [
       "-Max(0, -y, y) + Max(1, -y, y)"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 求边际密度函数 p_{Y}(y)\n",
    "from sympy import *\n",
    "x = symbols('x')\n",
    "y = symbols('y')\n",
    "p_xy = Piecewise((1,And(x>0,x<1,y<x,y>-x)),(0,True))\n",
    "integrate(p_xy, (x, -oo, oo))   ## 由于|y|<x,0<x<1时，因此y肯定在(-1,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b55c8f8",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "（2.3）边际分布列\n",
    "\n",
    "在二维离散随机变量 $(X, Y)$ 的联合分布列 $\\left\\{P\\left(X=x_{i}, Y=y_{j}\\right)\\right\\}$ 中， 对 $j$ 求和所得的分布列\n",
    "$$\n",
    "\\sum_{j=1}^{\\infty} P\\left(X=x_{i}, Y=y_{j}\\right)=P\\left(X=x_{i}\\right), \\quad i=1,2, \\cdots\n",
    "$$\n",
    "被称为 $X$ 的边际分布列。 类似地， 对 $i$ 求和所得的分布列\n",
    "$$\n",
    "\\sum_{i=1}^{\\infty} P\\left(X=x_{i}, Y=y_{j}\\right)=P\\left(Y=y_{j}\\right), \\quad j=1,2, \\cdots\n",
    "$$\n",
    "被称为 $Y$ 的边际分布列。\n",
    "\n",
    "例子：设二维随机变量 $(X, Y)$ 有如下的联合分布列\n",
    "\n",
    "<div>\n",
    "<img src=\"./images/10.png\" width=\"600\" align=\"middle\"/>\n",
    "</div>\n",
    "\n",
    "求$X$，$Y$的边际分布列。\n",
    "\n",
    "解：\n",
    "\n",
    "<div>\n",
    "<img src=\"./images/11.png\" width=\"600\" align=\"middle\"/>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6078014",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "（3）条件分布（非重点，了解）\n",
    "\n",
    "在概率的计算中，我们知道概率可以分为无条件概率和条件概率，而概率又是对随机事件发生可能性大小的描述；后来，我们使用随机变量描述随机事件，使用分布函数/密度函数/分布列计算随机事件发生的概率，因此条件概率理所当然的有条件分布/条件密度函数/条件分布列，那如何计算条件分布呢？我们可以参照条件概率的计算定义条件分布函数：\n",
    "\n",
    "- 多维离散随机变量的条件分布列：\n",
    "\n",
    "对一切使 $P\\left(Y=y_{j}\\right)=p_{. j}=\\sum_{i=1}^{\\infty} p_{i j}>0$ 的 $y_{j}$， 称\n",
    "$$\n",
    "p_{i \\mid j}=P\\left(X=x_{i} \\mid Y=y_{j}\\right)=\\frac{P\\left(X=x_{i}, Y=y_{j}\\right)}{P\\left(Y=y_{j}\\right)}=\\frac{p_{i j}}{p_{\\cdot j}}, \\quad i=1,2, \\cdots\n",
    "$$\n",
    "为给定 $Y=y_{j}$ 条件下 $X$ 的条件分布列。\n",
    "\n",
    "同理， 对一切使 $P\\left(X=x_{i}\\right)=p_{i}=\\sum_{j=1}^{\\infty} p_{i j}>0$ 的 $x_{i}$， 称\n",
    "$$\n",
    "p_{j i i}=P\\left(Y=y_{j} \\mid X=x_{i}\\right)=\\frac{P\\left(X=x_{i}, Y=y_{j}\\right)}{P\\left(X=x_{i}\\right)}=\\frac{p_{i j}}{p_{i} .}, \\quad j=1,2, \\cdots\n",
    "$$\n",
    "为给定 $X=x_{i}$ 条件下 $Y$ 的条件分布列。\n",
    "\n",
    "【例子】设在一段时间内进人某一商店的顾客人数 $X$ 服从泊松分布 $P(\\lambda)$， 每个顾客购买某种物品的概率为 $p$, 并且各个顾客是否购买该种物品相互独立， 求进入商店的顾客购买这种物品的人数 $Y$ 的分布列。\n",
    "\n",
    "解：\n",
    "由题意知：\n",
    "$$\n",
    "P(X=m)=\\frac{\\lambda^{m}}{m !} \\mathrm{e}^{-\\lambda}, \\quad m=0,1,2, \\cdots\n",
    "$$\n",
    "在进人商店的人数 $X=m$ 的条件下， 购买某种物品的人数 $Y$ 的条件分布为二项分布 $b(m, p)$, 即\n",
    "$$\n",
    "P(Y=k \\mid X=m)=\\left(\\begin{array}{l}\n",
    "m \\\\\n",
    "k\n",
    "\\end{array}\\right) p^{k}(1-p)^{m-k}, \\quad k=0,1,2, \\cdots, m .\n",
    "$$\n",
    "由全概率公式有\n",
    "$$\n",
    "\\begin{aligned}\n",
    "P(Y=k) &=\\sum_{m=k}^{\\infty} P(X=m) P(Y=k \\mid X=m) \\\\\n",
    "&=\\sum_{m=k}^{\\infty} \\frac{\\lambda^{m}}{m !} \\mathrm{e}^{-\\lambda} \\cdot \\frac{m !}{k !(m-k) !} p^{k}(1-p)^{m-k}\n",
    "\\end{aligned}\n",
    "$$\n",
    "具体的计算化简，我们交给Sympy进行："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "2d239aaf",
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\lambda^{k} p^{k} e^{- \\lambda} e^{- \\lambda \\left(p - 1\\right)}}{k!}$"
      ],
      "text/plain": [
       "lamda**k*p**k*exp(-lamda)*exp(-lamda*(p - 1))/factorial(k)"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 求际密度函数 p_{Y}(y)\n",
    "from sympy import *\n",
    "from sympy.abc import lamda,m,p,k\n",
    "x = symbols('x')\n",
    "y = symbols('y')\n",
    "f_p = lamda**m/factorial(m)*E**(-lamda)*factorial(m)/(factorial(k)*factorial(m-k))*p**k*(1-p)**(m-k)\n",
    "summation(f_p, (m, k, +oo))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "247718a4",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "- 多维连续随机变量的条件密度函数：\n",
    "\n",
    "对一切使 $p_{y}(y)>0$ 的 $y$, 给定 $Y=y$ 条件下 $X$ 的条件密度函数分别为\n",
    "$$\n",
    "\\begin{aligned}\n",
    "p(x \\mid y)=\\frac{p(x, y)}{p_{Y}(y)} .\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a99f03e",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "（3.1）连续场合的全概率公式与贝叶斯公式（拓展）\n",
    "\n",
    "- 全概率公式：\n",
    "$$\n",
    "\\begin{aligned}\n",
    "&p_{Y}(y)=\\int_{-\\infty}^{\\infty} p_{X}(x) p(y \\mid x) \\mathrm{d} x \\\\\n",
    "&p_{\\chi}(x)=\\int_{-\\infty}^{\\infty} p_{Y}(y) p(x \\mid y) \\mathrm{d} y .\n",
    "\\end{aligned}\n",
    "$$\n",
    "- 贝叶斯公式：\n",
    "$$\n",
    "\\begin{aligned}\n",
    "&p(x \\mid y)=\\frac{p_{X}(x) p(y \\mid x)}{\\int_{-\\infty}^{\\infty} p_{X}(x) p(y \\mid x) \\mathrm{d} x},\\\\\n",
    "&p(y \\mid x)=\\frac{p_{Y}(y) p(x \\mid y)}{\\int_{-\\infty}^{\\infty} p_{Y}(y) p(x \\mid y) \\mathrm{d} y} .\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64407870",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### 6. 多维随机变量的数字特征：期望向量、协方差与协方差矩阵、相关系数与相关系数矩阵、条件期望"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f216e5e6",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "（1）期望向量：\n",
    "\n",
    "期望向量是期望在多维随机变量的推广，具体来说：\n",
    "\n",
    "记 $n$ 维随机向量为 $\\boldsymbol{X}=\\left(X_{1}, X_{2}, \\cdots, X_{n}\\right)^{\\prime}$, 若其每个分量的数学期望都存在， 则称\n",
    "$$\n",
    "E(\\boldsymbol{X})=\\left(E\\left(X_{1}\\right), E\\left(X_{2}\\right), \\cdots, E\\left(X_{n}\\right)\\right)^{\\prime}\n",
    "$$\n",
    "为 $n$ 维随机向量 $\\boldsymbol{X}$ 的数学期望向量（一般为列向量）， 简称为 $\\boldsymbol{X}$ 的数学期望。至此我们可以看出， $n$ 维随机向量的数学期望是各分量的数学期望组成的向量。\n",
    "\n",
    "（2）协方差与协方差矩阵：\n",
    "\n",
    "（2.1）协方差：\n",
    "\n",
    "在多维随机变量中，我们往往需要衡量两个随机变量之间的相互关联的程度，衡量的指标就是协方差。在一维随机变量中，我们使用方差衡量随机变量X自身与自身的变化情况，我们的定义方式是：$Var(X) = E[(X-E(X))^2] = E[(X - E(X))(X - E(X))]$。那么理所当然的，衡量随机变量X与随机变量Y之间的关联程度就是：\n",
    "$$\n",
    "\\operatorname{Cov}(X, Y)=E[(X-E(X))(Y-E(Y))]\n",
    "$$\n",
    "仔细观察上述定义式，可知：如果两个变量的变化趋势一致，也就是说如果其中一个大于自身的期望值时另外一个也大于自身的期望值，那么两个变量之间的协方差就是正值；如果两个变量的变化趋势相反，即其中一个变量大于自身的期望值时另外一个却小于自身的期望值，那么两个变量之间的协方差就是负值。即：\n",
    "- 当 $\\operatorname{Cov}(X, Y)>0$ 时， 称 $X$ 与 $Y$ 正相关， 这时两个偏差 $(X-E(X))$ 与 $(Y-E(Y))$ 有**同时增加或同时减少的倾向**。 由于 $E(X)$ 与 $E(Y)$ 都是常数， 故等价于 $X$ 与 $Y$ 有同时增加或同时减少的倾向， 这就是正相关的含义。\n",
    "- 当 $\\operatorname{Cov}(X, Y)<0$ 时， 称 $X$ 与 $Y$ 负相关, 这时**有 $X$ 增加而 $Y$ 减少的倾向， 或有 $Y$ 增加而 $X$ 减少的倾向**， 这就是负相关的含义。\n",
    "- 当 $\\operatorname{Cov}(X, Y)=0$ 时，称 $X$ 与 $Y$ 不相关。 这时可能由两类情况导致:一类是 $X$ 与 $Y$ 的取值毫无关联， 另一类是 $X$ 与 $Y$ 间存有某种非线性关系。\n",
    "\n",
    "下面，给出协方差的性质：(与方差对比)\n",
    "- $\\operatorname{Cov}(X, Y)=E(X Y)-E(X) E(Y)$\n",
    "- 若随机变量 $X$ 与 $Y$ 相互独立， 则 $\\operatorname{Cov}(X, Y)=0$， 反之不成立。\n",
    "- （最重要）对任意二维随机变量 $(X, Y)$， 有\n",
    "$$\n",
    "\\operatorname{Var}(X \\pm Y)=\\operatorname{Var}(X)+\\operatorname{Var}(Y) \\pm 2 \\operatorname{Cov}(X, Y)\n",
    "$$\n",
    "这个性质表明: 在 $X$ 与 $Y$ 相关的场合,和的方差不等于方差的和。 $X$ 与 $Y$ 的正相关会增加和的方差,负相关会减少和的方差，而在 $X$ 与 $Y$ 不相关的场合，和的方差等于方差的和，即：**若 $X$ 与 $Y$ 不相关**， 则 $\\operatorname{Var}(X \\pm Y)=\\operatorname{Var}(X)+\\operatorname{Var}(Y)$。\n",
    "- 协方差 $\\operatorname{Cov}(X, Y)$ 的计算与 $X, Y$ 的次序无关， 即\n",
    "$$\n",
    "\\operatorname{Cov}(X, Y)=\\operatorname{Cov}(Y, X) .\n",
    "$$\n",
    "- 任意随机变量 $X$ 与常数 $a$ 的协方差为零，即\n",
    "$$\n",
    "\\operatorname{Cov}(X, a)=0 \n",
    "$$\n",
    "- 对任意常数 $a, b$， 有\n",
    "$$\n",
    "\\operatorname{Cov}(a X, b Y)=a b \\operatorname{Cov}(X, Y) .\n",
    "$$\n",
    "- 设 $X, Y, Z$ 是任意三个随机变量,则\n",
    "$$\n",
    "\\operatorname{Cov}(X+Y, Z)=\\operatorname{Cov}(X, Z)+\\operatorname{Cov}(Y, Z) \n",
    "$$\n",
    "\n",
    "【例子】设二维随机变量 $(X, Y)$ 的联合密度函数为\n",
    "$$\n",
    "p(x, y)= \\begin{cases}3 x, & 0<y<x<1, \\\\ 0, & \\text { 其他. }\\end{cases}\n",
    "$$\n",
    "试求 $\\operatorname{Cov}(X, Y)$。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "fb9cbcae",
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{3}{160}$"
      ],
      "text/plain": [
       "3/160"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 求协方差\n",
    "from sympy import *\n",
    "from sympy.abc import lamda,m,p,k\n",
    "x = symbols('x')\n",
    "y = symbols('y')\n",
    "p_xy = Piecewise((3*x,And(y>0,y<x,x<1)),(0,True))\n",
    "E_xy = integrate(x*y*p_xy, (x, -oo, oo),(y,-oo,oo))\n",
    "E_x = integrate(x*p_xy, (x, -oo, oo),(y,-oo,oo))\n",
    "E_y = integrate(y*p_xy, (x, -oo, oo),(y,-oo,oo))\n",
    "E_xy - E_x*E_y"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95ed70f5",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "【例子】设二维随机变量 $(X, Y)$ 的联合密度函数为\n",
    "$$\n",
    "p(x, y)= \\begin{cases}\\frac{1}{3}(x+y), & 0<x<1,0<y<2, \\\\ 0, & \\text { 其他. }\\end{cases}\n",
    "$$\n",
    "试求 $\\operatorname{Var}(2 X-3 Y+8)$。\n",
    "\n",
    "解：\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\operatorname{Var}(2 X-3 Y+8) &=\\operatorname{Var}(2 X)+\\operatorname{Var}(3 Y)-2 \\operatorname{Cov}(2 X, 3 Y) \\\\\n",
    "&=4 \\operatorname{Var}(X)+9 \\operatorname{Var}(Y)-12 \\operatorname{Cov}(X, Y)\n",
    "\\end{aligned}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "52a4a80e",
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 3.02469135802469$"
      ],
      "text/plain": [
       "3.02469135802469"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 方法一：先计算边际密度函数，在计算特征数\n",
    "from sympy import *\n",
    "x = symbols('x')\n",
    "y = symbols('y')\n",
    "p_xy = Piecewise((1/3*(x+y),And(x>0,x<1,y>0,y<2)),(0,True))\n",
    "p_x = integrate(p_xy, (y, -oo, oo))  # x边际密度函数\n",
    "p_y = integrate(p_xy, (x, -oo, oo))  # y边际密度函数\n",
    "E_x2 = integrate(x**2*p_x, (x, -oo, oo))\n",
    "E_x = integrate(x*p_x, (x, -oo, oo))\n",
    "E_y2 = integrate(y**2*p_y, (y,-oo,oo))\n",
    "E_y = integrate(y*p_y, (y,-oo,oo))\n",
    "E_xy = integrate(x*y*p_xy, (x, -oo, oo),(y,-oo,oo))\n",
    "cov_xy = E_xy - E_x*E_y\n",
    "var_x = E_x2 - E_x**2\n",
    "var_y = E_y2 - E_y**2\n",
    "var_2x_3y_8 = 4*var_x + 9*var_y -12*cov_xy\n",
    "var_2x_3y_8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "eb5701d9",
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 3.02469135802469$"
      ],
      "text/plain": [
       "3.02469135802469"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 方法二：直接通过联合密度函数计算特征数\n",
    "from sympy import *\n",
    "x = symbols('x')\n",
    "y = symbols('y')\n",
    "p_xy = Piecewise((1/3*(x+y),And(x>0,x<1,y>0,y<2)),(0,True))\n",
    "E_x2 = integrate(x**2*p_xy, (x, -oo, oo),(y, -oo, oo))\n",
    "E_x = integrate(x*p_xy, (x, -oo, oo),(y, -oo, oo))\n",
    "E_y2 = integrate(y**2*p_xy, (x, -oo, oo),(y,-oo,oo))\n",
    "E_y = integrate(y*p_xy, (x, -oo, oo),(y,-oo,oo))\n",
    "E_xy = integrate(x*y*p_xy, (x, -oo, oo),(y,-oo,oo))\n",
    "cov_xy = E_xy - E_x*E_y\n",
    "var_x = E_x2 - E_x**2\n",
    "var_y = E_y2 - E_y**2\n",
    "var_2x_3y_8 = 4*var_x + 9*var_y -12*cov_xy\n",
    "var_2x_3y_8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "7165b4b6",
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 3.02469135802468$"
      ],
      "text/plain": [
       "3.02469135802468"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 方法三：令z=2*x-3*y+8,使用VAR(Z) = E（Z**2）- E（Z）**2\n",
    "from sympy import *\n",
    "x = symbols('x')\n",
    "y = symbols('y')\n",
    "p_xy = Piecewise((1/3*(x+y),And(x>0,x<1,y>0,y<2)),(0,True))\n",
    "E_z2 = integrate((2*x-3*y+8)**2*p_xy, (x, -oo, oo),(y, -oo, oo))\n",
    "E_z = integrate((2*x-3*y+8)*p_xy, (x, -oo, oo),(y, -oo, oo))\n",
    "E_z2 - E_z**2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c036ad0b",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "（2.2）协方差矩阵：\n",
    "\n",
    "假设$n$ 维随机向量为 $\\boldsymbol{X}=\\left(X_{1}, X_{2}, \\cdots, X_{n}\\right)^{\\prime}$的期望向量为：\n",
    "$$\n",
    "E(\\boldsymbol{X})=\\left(E\\left(X_{1}\\right), E\\left(X_{2}\\right), \\cdots, E\\left(X_{n}\\right)\\right)^{\\prime}\n",
    "$$\n",
    "那么，我们把\n",
    "$$\n",
    "\\begin{aligned}\n",
    "& E\\left[(\\boldsymbol{X}-E(\\boldsymbol{X}))(\\boldsymbol{X}-E(\\boldsymbol{X}))^{\\prime}\\right] \\\\\n",
    "=&\\left(\\begin{array}{cccc}\n",
    "\\operatorname{Var}\\left(X_{1}\\right) & \\operatorname{Cov}\\left(X_{1}, X_{2}\\right) & \\cdots & \\operatorname{Cov}\\left(X_{1}, X_{n}\\right) \\\\\n",
    "\\operatorname{Cov}\\left(X_{2}, X_{1}\\right) & \\operatorname{Var}\\left(X_{2}\\right) & \\cdots & \\operatorname{Cov}\\left(X_{2}, X_{n}\\right) \\\\\n",
    "\\vdots & \\vdots & & \\vdots \\\\\n",
    "\\operatorname{Cov}\\left(X_{n}, X_{1}\\right) & \\operatorname{Cov}\\left(X_{n}, X_{2}\\right) & \\cdots & \\operatorname{Var}\\left(X_{n}\\right)\n",
    "\\end{array}\\right)\n",
    "\\end{aligned}\n",
    "$$\n",
    "为该随机向量的方差-协方差矩阵，简称协方差阵，记为 $\\operatorname{Cov}(\\boldsymbol{X})$。\n",
    "\n",
    "注意：$n$ 维随机向量的协方差矩阵 $\\operatorname{Cov}(\\boldsymbol{X})=\\left(\\operatorname{Cov}\\left(X_{i}, X_{j}\\right)\\right)_{n \\times n}$ 是一个**对称的非负定矩阵**。\n",
    "\n",
    "【例子】设二维随机变量 $(X, Y)$ 的联合密度函数为\n",
    "$$\n",
    "p(x, y)= \\begin{cases}\\frac{1}{3}(x+y), & 0<x<1,0<y<2, \\\\ 0, & \\text { 其他. }\\end{cases}\n",
    "$$\n",
    "试求 $(x, y)$的协方差矩阵。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "34538b3f",
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.0802469135802468 & -0.0123456790123456\\\\-0.0123456790123456 & 0.283950617283951\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[ 0.0802469135802468, -0.0123456790123456],\n",
       "[-0.0123456790123456,   0.283950617283951]])"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 求协方差矩阵：1.求两两变量的协方差和各自的方差；2. 组合成矩阵\n",
    "from sympy import *\n",
    "x = symbols('x')\n",
    "y = symbols('y')\n",
    "p_xy = Piecewise((1/3*(x+y),And(x>0,x<1,y>0,y<2)),(0,True))\n",
    "p_x = integrate(p_xy, (y, -oo, oo))  # x边际密度函数\n",
    "p_y = integrate(p_xy, (x, -oo, oo))  # y边际密度函数\n",
    "E_x2 = integrate(x**2*p_x, (x, -oo, oo))\n",
    "E_x = integrate(x*p_x, (x, -oo, oo))\n",
    "E_y2 = integrate(y**2*p_y, (y,-oo,oo))\n",
    "E_y = integrate(y*p_y, (y,-oo,oo))\n",
    "E_xy = integrate(x*y*p_xy, (x, -oo, oo),(y,-oo,oo))\n",
    "cov_xy = E_xy - E_x*E_y\n",
    "var_x = E_x2 - E_x**2\n",
    "var_y = E_y2 - E_y**2\n",
    "Matrix([[var_x,cov_xy],[cov_xy,var_y]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd03b8f4",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "（3）相关系数与相关系数矩阵：\n",
    "\n",
    "（3.1）相关系数：\n",
    "\n",
    "相关系数也是衡量两个随机变量之间的相关关系的特征数，前面所说的协方差也是衡量这个随机变量的相关性大小的，这两者有什么区别呢？协方差并没有排除量纲对数值大小的影响，这样的缺点就是两个协方差之间无法比较相关性的大小。比如：$X$和$Y$与$Z$的相关性如果使用协方差去衡量，那么就不能通过比较$Cov(X,Z)$与$Cov(Y,Z)$的大小来观察$X$和$Y$哪个与$Z$最相关。相关系数就是去除量纲影响后的协方差，具体来说：\n",
    "\n",
    "设 $(X, Y)$ 是一个二维随机变量， 且 $\\operatorname{Var}(X)=\\sigma_{X}^{2}>0, \\operatorname{Var}(Y)=\\sigma_{Y}^{2}>0$.\n",
    "则称\n",
    "$$\n",
    "\\operatorname{Corr}(X, Y)=\\frac{\\operatorname{Cov}(X, Y)}{\\sqrt{\\operatorname{Var}(X)} \\sqrt{\\operatorname{Var}(Y)}}=\\frac{\\operatorname{Cov}(X, Y)}{\\sigma_{X} \\sigma_{Y}}\n",
    "$$\n",
    "为 $X$ 与 $Y$ 的 **(线性)** 相关系数。\n",
    "\n",
    "相关系数的性质：\n",
    "   - $-1 \\leqslant \\operatorname{Corr}(X, Y) \\leqslant 1$， 或 $|\\operatorname{Corr}(X, Y)| \\leqslant 1$。\n",
    "   - $\\operatorname{Corr}(X, Y)=\\pm 1$ 的充要条件是 $X$ 与 $Y$ 间几乎处处有线性关系, 即存 在 $a(\\neq 0)$ 与 $b$， 使得\n",
    "   $$\n",
    "    P(Y=a X+b)=1 \n",
    "   $$\n",
    "   - 相关系数 $\\operatorname{Corr}(X, Y)$ 刻画了 $X$ 与 $Y$ 之间的线性关系强弱， 因此也常称其为 “线性相关系数”。\n",
    "   - 若 $\\operatorname{Corr}(X, Y)=0$， 则称 $X$ 与 $Y$ 不相关。不相关是指 $X$ 与 $Y$ 之间没有线性关系， 但 $X$ 与 $Y$ 之间可能有其他的函数关系， 譬如平方关系、对数关系等。\n",
    "   - 若 $\\operatorname{Corr}(X, Y)=1$， 则称 $X$ 与 $Y$ 完全正相关； 若 $\\operatorname{Corr}(X, Y)=-1$， 则称 $X$ 与 $Y$ 完全负相关。\n",
    "   - 若 $0<|\\operatorname{Corr}(X, Y)|<1$， 则称 $X$ 与 $Y$ 有 “一定程度” 的线性关系。 $|\\operatorname{Corr}(X, Y)|$ 越接近于 1， 则线性相关程度越高； $|\\operatorname{Corr}(X, Y)|$ 越接近于 0 ， 则线性相关程度越低。 而协方差看不出这一点， 若协方差很小， 而其两个标准差 $\\sigma_{X}$ 和 $\\sigma_{Y}$ 也很小， 则其比值就不一定很小。\n",
    "   \n",
    "（3.2）相关系数矩阵：\n",
    "\n",
    "类似于协方差矩阵，相关系数矩阵就是把协方差矩阵中每个元素替换成相关系数，具体来说就是：\n",
    "$$\n",
    "\\begin{aligned}\n",
    "& \\operatorname{Corr}(X, Y)=\\frac{\\operatorname{Cov}(X, Y)}{\\sqrt{\\operatorname{Var}(X)} \\sqrt{\\operatorname{Var}(Y)}}=\\frac{\\operatorname{Cov}(X, Y)}{\\sigma_{X} \\sigma_{Y}} \\\\\n",
    "=&\\left(\\begin{array}{cccc}\n",
    "1 & \\operatorname{Corr}\\left(X_{1}, X_{2}\\right) & \\cdots & \\operatorname{Corr}\\left(X_{1}, X_{n}\\right) \\\\\n",
    "\\operatorname{Corr}\\left(X_{2}, X_{1}\\right) & 1 & \\cdots & \\operatorname{Corr}\\left(X_{2}, X_{n}\\right) \\\\\n",
    "\\vdots & \\vdots & & \\vdots \\\\\n",
    "\\operatorname{Corr}\\left(X_{n}, X_{1}\\right) & \\operatorname{Corr}\\left(X_{n}, X_{2}\\right) & \\cdots & 1\n",
    "\\end{array}\\right)\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "【例子】设二维随机变量 $(X, Y)$ 的联合密度函数为\n",
    "$$\n",
    "p(x, y)= \\begin{cases}\\frac{1}{3}(x+y), & 0<x<1,0<y<2, \\\\ 0, & \\text { 其他. }\\end{cases}\n",
    "$$\n",
    "试求 $(x, y)$的相关系数矩阵。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "5ff86642",
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & -0.0817860820109527\\\\-0.0817860820109527 & 1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[                  1, -0.0817860820109527],\n",
       "[-0.0817860820109527,                   1]])"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 求相关系数矩阵：1.求两两变量的相关系数；2. 组合成矩阵\n",
    "from sympy import *\n",
    "x = symbols('x')\n",
    "y = symbols('y')\n",
    "p_xy = Piecewise((1/3*(x+y),And(x>0,x<1,y>0,y<2)),(0,True))\n",
    "p_x = integrate(p_xy, (y, -oo, oo))  # x边际密度函数\n",
    "p_y = integrate(p_xy, (x, -oo, oo))  # y边际密度函数\n",
    "E_x2 = integrate(x**2*p_x, (x, -oo, oo))\n",
    "E_x = integrate(x*p_x, (x, -oo, oo))\n",
    "E_y2 = integrate(y**2*p_y, (y,-oo,oo))\n",
    "E_y = integrate(y*p_y, (y,-oo,oo))\n",
    "E_xy = integrate(x*y*p_xy, (x, -oo, oo),(y,-oo,oo))\n",
    "cov_xy = E_xy - E_x*E_y\n",
    "var_x = E_x2 - E_x**2\n",
    "var_y = E_y2 - E_y**2\n",
    "corr_xy = cov_xy/(sqrt(var_x*var_y))\n",
    "Matrix([[1,corr_xy],[corr_xy,1]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "899a0dee",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### 7. 随机变量序列的收敛状态：依概率收敛、依分布收敛"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68906f68",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "在之前的学习中，我们学习了概率论的基本概念、一维随机变量及其相关的概率密度函数、分布函数、分布列以及数字特征、多维随机变量的联合密度函数、联合分布函数、联合分布列以及数字特征等，下面来总结下这些概念之间的关系：\n",
    "\n",
    "<div>\n",
    "<img src=\"./images/12.svg\" width=\"800\" align=\"middle\"/>\n",
    "</div>\n",
    "\n",
    "- 在随机现象和概率的讨论中，我们主要学习了**样本点**与**样本空间**，并由样本点的集合构成**随机事件**，主要目的是计算某个随机事件的**概率**，其中有一类特殊的概率叫**条件概率**，由条件概率延伸出的三大公式：**乘法公式**、**全概率公式**以及**贝叶斯公式**。\n",
    "- 在一维随机变量的讨论中，我们为什么会设计随机变量呢？是因为我们想用数理的形式研究这些随机事件及其概率，用文字表示的随机事件多麻烦呀，而且数理形式还能使用高等数学的理论研究，如：极限、微分学、积分学等。**因此，随机变量诞生的目的其实就是为了将随机事件使用数轴范围表示出来，那随机变量每一个取值其实就是一个样本点，随机变量的定义域就是样本空间**。接下来，我们希望计算由随机变量表示的随机事件的概率，因为这才是我们的主要目的。因此，可以从两个角度去计算由随机变量表示的随机事件的概率，那就是使用概率直接计算的**分布函数**与间接使用密度计算的**密度函数/分布列**。在实际的现实应用上，记住一个函数或者使用计算机存储一个函数的各个取值是很困难的，而且有时候我们仅仅只需要知道随机变量的某个侧面的信息，因此**数字特征**就是这么诞生的。\n",
    "- 在多维随机变量（维度是有限的）的讨论中，有时候影响某件事概率的因素会有很多个，单一随机变量不足以表达完整信息，需要使用多个随机变量才能表达更多的信息，因此根据线性代数的理论，将一维推广至多维可以使用向量/矩阵表达，**多维随机变量/随机向量**就此诞生。同时，我们需要将一维随机变量的所有理论推广至多维，因此**联合密度函数、联合分布列与联合分布函数**就此出现。多维随机变量的数字特征也由原来的单一的一个随机变量的数字特征推广至两个变量之间的数字特征，如**协方差、相关系数**等等。\n",
    "\n",
    "因此，我们在这里更进一步，将随机变量的维度推广至无穷维，我们想要研究随机变量的序列在数量$n \\rightarrow \\infty$会怎么养变化，会不会出现什么规律。在高等数学中，我们是使用“极限“这个工具研究$n \\rightarrow \\infty$的情况，那么概率论借用了这个理论，也是使用”极限“研究随机变量序列在数量$n \\rightarrow \\infty$时的变化规律。\n",
    "\n",
    "（1）依概率收敛：\n",
    "\n",
    "在前面的学习中，我们有一个观点是：频率可以近似地看成概率，这个观点十分直观但是并没有告诉我们频率什么时候可以近似概率。事实上，频率是概率的**稳定值**，又或者说频率**稳定于**概率。下面，我们通过几个例子来看看什么是“稳定”：\n",
    "\n",
    "设有一大批产品， 其不合格品率为 $p$。 现一个接一个地检查产品的合格性，记前 $n$ 次检查发现 $S_{n}$ 个不合格品, 而 $v_{n}=\\frac{S_{n}}{n} $ 为不合格品出现的频率。 当检查继续下去， 我们就发现频率序列 $\\left\\{v_{n}\\right\\}$ 有如下两个现象：\n",
    "（1）频率 $v_{n}$ 对概率 $p$ 的绝对偏差 $\\left|v_{n}-p\\right|$ 将随 $n$ 增大而呈现逐渐减小的趋势， 但无法说它收玫于零。\n",
    "\n",
    "（2）由于频率的随机性，绝对偏差 $\\left|v_{n}-p\\right|$ 时大时小。 虽然我们无法排除大偏差发生的可能性, **但随着 $n$ 不断增大， 大偏差发生的可能性会越来越小**。这是一种新的极限概念。\n",
    "\n",
    "事实上，之前我们也做过这个实验，下面来回顾下：\n",
    "\n",
    "【例子】频率近似概率："
   ]
  },
  {
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   "execution_count": 118,
   "id": "761adfe8",
   "metadata": {
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   "outputs": [
    {
     "data": {
      "image/png": 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t+iujpkbBYtHqYTCcXSfm26vNm03U1yukpqqce277+hs5GZWVCgsXJnDwoJE9e4ykpqr88pd1DBhw9tVZF8HfXFdPbe2Jg3/BgnhKS01ccombgQNbbrIG5+jJympfLX6AMWPqOXrUwDXX1JOWpvLyy1WoKixZEse//53Itm0mFi1KoKbGwHvvWXn00RoUBV59NZGNG098IVhycoAePXx89FECF1/swW7X3oyyMgOrV8exfHkctbUKI0e6WLQogbFjnfz85y4qKgykp5/el4DPp32xdO4c2Qn3Dz+MZ+5ca+j2eed5uf76erp184dGg1VVGULXZNTXK7z/fgJDh3piOtBOlcOh8OabVlatigvdN2yYtkbF0KFuUlJUjhwxcOiQgf79fS2+1xUVBmy2QGhRorON06mwcGE8n30Wj8ejLZTUv7+XI0cMPPNMCiaTSna2n3HjnBFN3eL1woYNZrp29Uf82T1ZZ+lL2boad/WczMndefO0EFi71sLLL1eFnut0KjgcSmgx87IyI3a7n4R2OA1O374+nnzyaNh9igKXXurmww8TePXVRMrLjfTq5WPXLhMbN5pJSlIjCn2AX/5S+7BPnWpj9mwrv/iFk7lzrXzzTcPzExJUFi1KwGRSWbAgAVXVXvuf/ayeG288+YVkamoUli6NY/NmMyUlZn7721p69/axfbsJi0Wlb18f5h97sVRVC5bNm81hoQ+wbZuZbdvMZGX5eeSRGt57L4GlS+OZMKGOiy9289xzyZSUmPjqqzimTq2hZ8/wL36HQ8HtVpg3L4FevXxccUX7OAcUCb+/6S+iujqFd96xsmuXCbNZpbzcQH29wpVXukhODrB/v5EVK7QvgY8/jueSS9wUFWlhaTZrCw3dfnsdmZkBDh828J//WDlwwMihQ0Y6d/YzebIDuz28HFVVCnV1BhTlzDa8jh5VWLvWQkWFgS++iMPhMDB0qJuxY+tDI/u8Xvjss3iKi83s32/k6adTuPBCD7/4hZOOHQMcPGjEaNR+XQYbWzt3mn/8FWzAYFC57DI3Eye2fvl1EfzHXsAFkbX4G6uoMGC1ajuaMyeB9estPPXUUaZPT+b7701ccEGU5oFoIxYLjB7t4j//sZKeHuChh2r44x9tzJ2bgNkMNluA6dOriYvTflF5veB2K/j92vDZ2loFh8NAbq62ZOSYMfW8/74WCsFutk6d/Iwc6SI1VeWjj+KZOLGOZ59NZt48KyaTysKFCZx/vjfi1rTPp/33t78ls2uX9tFOSQnw8stJpKcHQr/MevXykZfn5eqr65k3z0phoTayKS/Py69/XRta+eyLL+JYsCCBsjIj//u/NqqrDdjtft58M5GiongOHjQwYUIdn3wSz1/+kkKPHn7MZq2by2SCnTtNoc/ZihVxOJ0K117b/q6aq61VCAQgJUVl+fI4iovNfPedifT0AFOmONiwQfvSPPZvqVs3Hw89VEd2dsMfYH6+m/JyAx9/nMCiRQmcf76Hnj39FBXFsX27mUcftXHJJW6++iouNJniJZe42brVzOOP20hKMpGbm4jFAt9+a8bpVEINu2HD3Nx8s5OkpIbL0n0+7XEA55zjD/3iDNqzx8jXX8cxcKCH5GTtF2ZGRiBs9bvGPB7tvNVHHyWEZgDIzfVy0021YfUEMJu1v6HRo12h5y1cmMAf/mAjJUWlujr8FKuiaOcgs7L83HZbHVu3mlm6NI7hwxXOOSfSdysyOgn+xi1+7Y0P9mO31OI/dkqDykpD6ORtWZmRqioDq1db+P577SUMzskTS4YPd7F2rZkrr3QRH6+F98yZSQBMnFgXWtwluExkfHzwRVPp2BGg4TUZNcrFV1/FsX+/kYsu8tCvn5eCgoYW8KBBntB+58xJYPLkOl58MYkZMxJ54okaEhKan2Ni3z4jdXUKNpvCyy+nsHevKbS/Pn28XHihlz/9KYUffjCSnh7A4VDYtcvErl0mVq+2sH+/9hfev7+Xe+6pDetOGD7czfDhbpYvt/D//l8SV17p4qabnDz7rNbSnzKljsGDPeTlaccIftk0lpoa4Je/dPLtt2bef9+K3w9jxpz94a+qsGWLCafTwBtvWFFVhXPO8bFlixainTr5OXDAyNSpNvx+BaNRJTvbx2231dGlix9V1c6VHBugffv66NtXe39KS4306qUNgb7uunoqKxVeey2JpUvjueACD7fe6sRm00LY6dR+TWzdag51HVksKjk5PjIy/NTVGfj6awvFxWZ69/ZhMmlBumeP9osh+Pif/MRDx44BLr7YTWFhPMuWxaOqhL78QftbHjzYTdeufgYO1BouqgqrVll4/30rFRUGLrzQw1VXubBa1SaB3xyLBX72MxeXX+5m/vwEDh82cvnlblRV27fBAD/9qZusrIYvpoEDvYwe7eLcc9OpqDjddzRcmwb/l19+yWWXXRb14zTX4g9qqcV/7P0VFQ3fzocPax+knTsbXr5YDP64OHj44YYFXIYO9bB4sQ+DQWtdnQyTCe69t5YdO8zk57tb7M9tvMDMnXfW8eSTKcyebWXy5Lqwx23ebGLtWgtLl2p/sBaLEY9Hez/GjKnnhhsauoimTq398Y/Vi6pCUVEcu3aZ+PrrOC66yMO99zowHGd826WXerjggiqSklQUBX73u1qqqgyhFdE6dgzwxBNHOXzYiMej4PNpn7mePf106KA9ZtAgD0aj1oXl9SqMHVt/1p44rqlRmDkzKTSqKztbe8937DBx881Oevf20rWrn5oarTtmwAAvI0Yc+54efzIoi4WwOa0A0tNVHniglkOHtNe28f6sVpU77qjDbk9g8+ZqVJUm/d/79hl57bVE1q9v6Ebs1MnPTTdpM9Tu2mVi5UrtS2PBggQMBpUrr3QxapTWwKmqMuD3K6xbZw518557ro8rrnDx6afxfP+9iexsH5MnO0550sWUFLXJjLnHc7rnuVoSteD3+XzMnj2bjIwMampqGD9+fGjbxIkTqa2tJS0t7YwHf7CfPqilFn9VVfPB7/E0XOFaXNww3DEWg/9YBgP84Q81GAwcNyhbkpUVICsr8i+Mc8/18bOf1fPhhwlccIGXn/zEw8aNZt56yxr68gWtOycQgJtuquPSS91NzrV07+4PLXqvKDBypJuCAjcFBS6ys/0R1SU5ueFzY7E0LIMZlJ6ukp7echgYDDBpUh1GozY1tt+vdQN89lk8w4e722wSP4dDYdasRDZssJCeHuDqq+tZtCgBh0PhJz/xkJ3t4+qrtes5tF9WDa9DfHyA++93tGp5FAUyM4//WrS0vVs3P48+WsPRowp+v4LBoA0uMDcalVxWpg29Xr/ewtChntB5gSuvbPhcjh0L+/aZKCszMmdOAjNmJJGaGmDSJAfDhnnO2i/sk6GoanTmafz000/ZuXMn9957L4899hhjx44lLy8PgNWrVzNgwAAURcFqtZ5gT5qq558Pu+3r2xfvBReA10vCvHlNHu/t3x/fgAHYrVbm/uKdUP/uHXc4eO21JHamDGRPUn+svqMMO/wh/z2hjjhLw0ux1fZT/vT2QFI85Qwp/4Tevb1kZfn54guthVmcOoyD1nNIcx9kUMVn3H67I+xnrXvYMAJZWRjKyohbsaJJ+dz5+QQyMjDu3Ytl1aqm20eOJJCejvG777CsW9dku+vqq1FTUjBt345548awbcnJyRzJz0dNSMC0eTPmLVuaPL/+hhvAbMa8YQOmHTuabv/FLwAwf/MNpt27wzeaTNSPHQuA5euvMZaWhm1W4+NxjRmjbf/yS4wHDoRvT07GNXo0AHFLl2I4fDhseyAtDfeVV2rHL/yUhf92UX6k4cWttHRirf1KLr/czQ3MpXPiUZKTk6mt1X6d+Dt3xvNjgyJ+wQKUY2aj83fvjmfoUAAS5s5tsmCDr2dPvIMGadvffbfJaxPpZ0+pryf+ww+bbJ+z56e8t3Vg6LOXmBjgoou8gHaiL+vG8/H37o2hspK4zz5r8nzPkCH4s7MxV/jY+cKH9O3jDX32jh41sC41n8Fj7ZgPHv+zd3DlD6x59tvQeYigXeddya0PxNPTu+OkP3sArp//PGqfveS0NA7/+NmI9mcv7tNP8R2q5uBBI507awMCAhkZuPPzAYhftAilNnxJ02h89hp/tk/2s5f2m980eQxEscVfXFxMZmYmADabjY0bN5KXl4fH4+HVV1/F7XYzePBgpkyZgqGZJldRURFFRUUATJs2jeTk5LDtamoqqt0OXi+GY7YBqGlpqHY7Jo8Hs9lChw4wPF/FZkvGYjFgNpuxWCxYFAsmkxG/L4nkDo2er6ZgsViYMN7I0beMeLxGNm8m1AdsidOen9vHzFi7gdTU8DIkpqeD3Q719c2WL7S9pub42ysqmt/eoQPYbChpaSjHbDcYDHTo0AGs1ma3AyTa7WA2o6Smtrwdmt9uMjVst9mabk9IIKnxdkd4q1BNSWnYnpKCUl/fZLsaOn4K117jY/bshs/IjTcamDTeQLduCSgfJKHUBDAYDKHPiGqzhZ5vSEkhrMl37Pbk5CZ/fKHPVnD7MSL97OF0Nrv91lsTUNabWPmJmRG5BlavNrJyZUMZO6V1oKelI7XfK+ybb+Oii1SsVujRQ+X77xXKd6VTW9ORRa+V02O7lb174JxzVFat0pqiGzrY+OZgJ6b+sr7hNfmxTRMIwNfrO1BSm8G2j50MNJoZf3OAzpnaCfqdOxWy7zFj7Z4GO9JO+rMX2h6lz57BYMB+pj57KSkoPh8dOhxn+zFlj8ZnL+yzfZqfvaCotfifffZZMjMz+a//+i+ef/55OnTowIQJEwgEArhcLrxeL4888gi33347AwcOPOH+9u/ff0rlsNvt/O53bgIB+MMftG/NKVPSQid3gx55pCZs9MjChfG8/76VGTMqeeONRL77zoTJBAcOaE2rnj197N5t4oYbnGfdyTq73U55eXlbF6NVlZcbQjOdNtct0h7rrKpafQ4e1IYEAhw6ZGTduoY+aotFDY1u6dbNx759DW21Tp3MXHHFUebOTQg95pxzfAwd6uG99xJITw/w6187qKlReOmlpCYt+5wcL3ff7Qjrvjnbtcf3+XSdTp27dOnS7P1Ra/Hn5uay48efcdXV1fTv3x+n04nVag1172RnZ5OamhqtIoQE/8CCLBa1SfDX1YXfPnrUQHy8Sny8FjRVVYbQuH3QhgTu3m2K2gUWItyxw/BiQfAzmZkZ4Be/0FqeqgrLlsWxYYN2/cDVV7tYvDieffuMbNhg4cILPWRm+jGZYOxYA4rion9/L999Z2L48IYTrL16efnHP5L5859TfjzZrBAfr2KxqFxzjQu73c8FF3jP2ouiRHRF7W0fMWIE+/bto7CwkJycHEpKSkhJScHhcLB7924uuugiBg0aRM+ePaNVhBC/X7tAJCguTvt3SkogNKb82OCvrjaQmqqFTYcOAXw+JTT0DyAzUzsp1Llz7J/UFWdOcLGc/PyGk43Bi9icTiVscILdnkh5uXZS89h5onr39vOnPx1lxowkEhNVJk2qazKwQehX1ILfZDIxadKkaO3+pAQC4aNQggugp6a2HPxVVeHB31h+vouLL/ZgsehjNI84O5xscKenq/zv/9ae+IFCd3QxO2fT4Nf+n5ra8IdUVxf+UlRXK6SlaYHfuJth8mQHt93mxGrVLqeOhaFdQgh90VHwNx6Hrf3bZmsI9Ob6+FNStMfZ7Q2t+ljsaxZC6Isugv/Yk7vBPv5gVw5oF7IEuVzg8SikpGjb4xuu5pbgF0K0e7oI/kBACbu4Kji0NtiVA+FdPcFhb8Hgb6zxc4QQoj3SSfA3f3K3pa6eo0e1fwe7eqBhArKWZu0TQoj2QhejeFvq42/c1dM4+B0O7VsiOblh+/Tp1a2yWpcQQrQ1XbT4m/bxa/9PSIB//auSK65whQV/cIhn4ysabTb1hJNHCSFEe6CL4A+uFhQUbPEHT/ImJqrU1Smh+UyCq3MlJUnQCyFij066epSw4A9exRvst09MVAkEFFwuhW3bTCxdGkdcnBo2mkcIIWKFToI/vMXfr5+XH37whK6ETEzUWvZ1dQp//7s2o13HjnJFrhAiNuko+Bv663v39tO7d8N0rcE1OhuP5W+88IYQQsQSXfTxH3ty91jBln/j4G+8YLMQQsQSXQR/IHD88ffB1n1wGCeAokjwCyFik06CXznuuqrB8fqHDjU8KBCQMftCiNikk+AP7+M/VlKSiqI0rK4VfI4QQsQiXQT/ifr4DQat1d84+IcNc7f8BCGEaMd0M6rnRPPm22wNwf+HP9TQt6/v+E8QQoh2Shctfr//+H38oJ3gdbvlil0hROyL+eBXVe2/EwV/4ymYExNlRI8QInbpIvgBjMbjh3njCdkk+IUQsSzmgz84OudEffzBIZ1xcWpooRYhhIhFugn+E3X1BFv8csWuECLWSfD/KNjilxO7QohYF/PB7/9xks1IT+4G5+0RQohYFbXg9/l8vPHGGyxatIh33nmnyfYdO3bw9NNPR+vwIQ0t/shO7kpXjxAi1kUt+JcsWYLD4WD06NFs27aN4uLi0LbS0lI+++wz3O7oXx0b6cndYBePdPUIIWJd1K7cLS4uJjMzEwCbzcbGjRvJy8vjwIEDHD58mAEDBrBs2bIWn19UVERRUREA06ZNw263n1I5amtNWCyQmmrEbj9+az4720hOjhG73XpKxzpbmEymU3692iupsz5InVtpn626txYoioL644D6+fPn43A4qKiooLy8nKKiIgoKCpo8p6CgIOz+8vLyUzy2HY8ngMNRR3n58X9hPP649svgFA911rDb7af8erVXUmd9kDqfnC5dujR7f9SCPzc3lx07dgBQXV1N//79cTqd3H333QAsW7aMZcuWNRv6rSnY1XO8+fiDTtQdJIQQsSBqffwjRozAarVSWFhITk4OJSUlYf38Z0pDH7+ctBVCCIhii99kMjFp0qQWtw8fPpzhw4dH6/AhkY7jF0IIvYj5OJTgF0KIcDEfhxL8QggRLqI49Hg8bN26FdDG4PuDl8O2A5FeuSuEEHoRURw+88wzzJs3D9D67mfMmBHVQrUmObkrhBDhIgr+vn37kpOTA0AgEGD16tVRLVRrCs7HLy1+IYTQRDSqp7S0lPr6ej744AOWLFnSrq6ckz5+IYQIF1Ecjhs3DpfLxdy5c0lISGDKlCnRLlerkeAXQohwEbX4DQYDDz/8MPHx8ZSVldGxY8dol6vVRDo7pxBC6EVE7eBnn32WyspKQJtw7Z///GdUC9WaAgFtHgZp8QshhCaiOBwwYEBosh+n08mGDRuiWaZWFem0zEIIoRcRdfV4PB5mzpxJYmIiq1atomvXrtEuV6uRPn4hhAgXURxOmDABRVFYv3493bp141e/+lW0y9VqJPiFECJcRC1+q9XK5MmTQ7fXr18fWmTlbCcXcAkhRLiIgv+tt96isLAQj8cTuu/dd9+NWqFak7T4hRAiXETBv3jxYsaNG0dycjIAmzdvjmqhWtPJLMQihBB6EFHwX3nllQwePJhOnToByMldIYRox04Y/Dt27GDdunV8/vnnJCYmAuBwOHjjjTeiXbZWIcEvhBDhThj8ffv2JT8/nz179tC5c2cAdu7cGfWCtRY1dE5XTu4KIQRE2NVz9dVX43K5SE5OxuFwMGrUqGiXq9UEg18u4BJCCE1EHSDvvPMO//jHPwDYt28fy5cvj2qhWpMEvxBChIso+J1OJ1lZWQB06tSJ+fPnR7VQrUmmbBBCiHARdfX4fD6MRiM7d+7kgw8+wNAOz5RK8AshhCai4B80aBAvvPACn332GSaTKewq3rOdtPiFECJcRME/ePBgZsyYwYEDB+jYsSMulyva5Wp17fBHihBCREVEwf/SSy+F3Xa5XPz2t7+NSoFaW7DFL4QQQhNR8G/evDl01a7L5SIlJeWEz/H5fMyePZuMjAxqamoYP348oC3WPnPmTL755huGDBlyxrqNpMUvhBCaiIL/3nvvpV+/fgCoqsrLL798wucsWbIEh8PBbbfdxmOPPUZxcTF5eXlUVlYyYcIE8vPz+fzzz0+v9BGQFr8QQoSLKPi3bt3K1q1bAaiqquLrr7/m7rvvPu5ziouLQ1M322w2Nm7cSF5eHna7nUOHDjFnzhyGDBnS4vOLioooKioCYNq0adjt9ogqdCyDwYjFYsRuTyc9/ZR20e6YTKZTfr3aK6mzPkidW2mfkTzoo48+IikpCQCz2cyYMWNO6iCKoqA2zJ2AyWTinnvuYerUqWRkZJCbm9vkOQUFBRQUFIRul5eXn9Qxg3y+jng8fioqqggE9DFtg91uP+XXq72SOuuD1PnkBJfMPVZEwT916tRQV0+kcnNz2bFjBwDV1dX0798fp9MJQIcOHQBISUkJTfwWLcHvG+njF0IITUTBn5GR0eI3zuLFi7nlllua3D9ixAj27dtHYWEhOTk5lJSUkJKSwsGDBykrK2PAgAGMGjWKnj17nl4NTkCmbBBCiHARBf8999xz3O3NBb/JZGLSpEmnVqpWJMEvhBDhIgp+u93OzTffTGpqKuXl5Xz99deMGTOGQCDA3Llzo13G0yLBL4QQ4SIK/gEDBjBs2DBAG4e/ePHiUJ9/RkZG9ErXClR9nM8VQoiIRRT8DoeDRx99lLS0NPbu3YvFYgltay/BLyd3hRBCE1Ec3nPPPWRnZ1NaWkrnzp25//77o1ys1iMtfiGECBdRi99kMnHxxRczadIkSktLQxdmtSeKIt8AQggBEbb4n3nmGebNmwdoXwIzZsyIaqFak5zcFUKIcBEFf9++fcnJyQG0k7urV6+OaqFakwS/EEKEi6irp7S0lPr6ej744AOWLFnSrubKkOAXQohwEbX4x40bh8vlYu7cuSQkJDBlypRol6vVSPALIUS4iFr8hw4dYtKkSWRnZ0e7PK1OVbXEl+AXQghNRC3+mTNnsnz58tDtysrKqBWotUmLXwghwp2wxb97927OO+889u/fz5w5cwDYtm0bjz76aNQL1xok+IUQIlyLwf/yyy8zYsQIzj33XDweD9u2bWPv3r0A1NXVnbECni4JfiGECNdi8G/ZsoUxY8agKAp5eXnceuutoXV3t2/ffsYKeLqCSy9K8AshhKbF4O/Tpw/bt29n9+7dbNq0CZPJxKZNmwgEAnzxxRc8+eSTZ7Kcp0VCXwghGrQY/DfffDMzZ85k8+bNBAIB1q5deybL1WpksXUhhAjXYvB37NiRhx9+GJ/Px4oVKxg+fHho29KlS89E2VqNwSDz9AghRNAJh3OaTKaw0AfIz8+PVnlaXSAgXT1CCNGYLmapl+AXQogGMR/80uIXQohwMR/8shCLEEKE00XwS4tfCCEaSPALIYTOSPALIYTOSPALIYTORDQf/6nw+XzMnj2bjIwMampqGD9+PAD19fXMmjWLkpISunTpwgMPPIDFYolWMX4MfjnDK4QQQVFr8S9ZsgSHw8Ho0aPZtm0bxcXFAGzatIk77riD5557jp07d1JWVhatIgDS4hdCiGNFrcVfXFxMZmYmADabjY0bN5KXl8fgwYMBqKqqokePHnTv3r3Z5xcVFVFUVATAtGnTTnmdX0UxEB8f167WCT5dJpNJV/UFqbNeSJ1baZ+turcWKIqC2mhAvdPpZNWqVUydOhWlheZ4QUEBBQUFodvl5eWndGy/PwOPx0N5efUpPb89stvtp/x6tVdSZ32QOp+cLl26NHt/1Lp6cnNzQ0s0VldXk5mZidPpxO12s27dOvLz86mpqWHJkiXRKgIgF3AJIcSxotbiHzFiBPv27aOwsJCcnBxKSkpISUnhwIEDvP3226HH3XvvvdEqAiB9/EIIcayoBb/JZGLSpEnNbrv++uujddgmJPiFECKcjOMXQgidkeAXQgidkeAXQgid0Unwy9AeIYQI0knwt3UphBDi7KGL4DfEfC2FECJyMR+JgUBbl0AIIc4uMR/8IF09QgjRWMwHv0zZIIQQ4WI++EH6+IUQorGYj0Tp4xdCiHAxH/wgLX4hhGgs5iMxEJALuIQQorGYD365gEsIIcJJ8AshhM7oIviFEEI00EXwS4tfCCEa6CD4FQl+IYRoRAfBLy1+IYRoTIJfCCF0RoJfCCF0RoJfCCF0RifBL2M6hRAiSCfB39alEEKIs0fUgt/n8/HGG2+waNEi3nnnnbBtmzZt4rHHHovWocNI8AshRLioBf+SJUtwOByMHj2abdu2UVxcDEBZWRmBQIDy8vJoHTqMXLkrhBDhTNHacXFxMZmZmQDYbDY2btxIXl4eWVlZmM3mEz6/qKiIoqIiAKZNm4bdbj+lciiKgcREK3Z73Ck9vz0ymUyn/Hq1V1JnfZA6t9I+W3VvLVAUBfUkm94FBQUUFBSEbp/qLwS/vxNut5Py8tpTen57ZLfbz9gvqrOF1FkfpM4np0uXLs3eH7WuntzcXCorKwGorq4mMzMTp9MZrcO1SPr4hRAiXNSCf8SIEVitVgoLC8nJyaGkpITi4mJ8Ph9r1qzB4XCwZcuWaB0+RIJfCCHCRa2rx2QyMWnSpGa3XXvttVx77bXROnQYVQWj8YwcSggh2gVdjOMXQgjRQBfBbzBI+gshRFDMB38g0NYlEEKIs0vMBz/IyV0hhGgs5oNfWvxCCBEu5oMfwKCLWgohRGRiPhIDAenqEUKIxmI++OUCLiGECCfBL4QQOiPBL4QQOqOT4JcLuIQQIkgnwd/WpRBCiLNHzAe/EEKIcDEf/NLiF0KIcBL8QgihMxL8QgihMxL8QgihMxL8QgihMxL8QgihMzoJfrmASwghgnQS/G1dCiGEOHvoIviFEEI00EXwS4tfCCEaSPALIYTO6CL4ZelFIYRoYIrWjn0+H7NnzyYjI4OamhrGjx9/3PujRfr4hRAiXNTawkuWLMHhcDB69Gi2bdtGcXHxce+Phg8+SKCuTpEWvxBCNBK1Fn9xcTGZmZkA2Gw2Nm7cSF5eXov3H6uoqIiioiIApk2bht1uP+kynHeeQiAABQVW7HbradSmfTGZTKf0erVnUmd9kDq30j5bdW8tUBQFtZk+l5buBygoKKCgoCB0u7y8/KSP27cvXHKJnfLyck7h6e2W3W4/pderPZM664PU+eR06dKl2fuj1gmSm5tLZWUlANXV1WRmZuJ0Opvcn5ubG60iCCGEaEbUgn/EiBFYrVYKCwvJycmhpKSE4uLiJvdfeOGF0SqCEEKIZkStq8dkMjFp0qRmt7V0vxBCiOiT8S5CCKEzEvxCCKEzEvxCCKEzEvxCCKEzEvxCCKEzitrSFVRCCCFiUsy3+H//+9+3dRHOOKmzPkid9SEadY754BdCCBFOgl8IIXQm5oO/8URveiF11gepsz5Eo85yclcIIXQm5lv8QgghwknwCyGEzkjwCyHEWeTLL7+M+jHOyApcZ9qZXtC9rWzatIk5c+bw+OOPU1VVxZw5c0hOTqZHjx4MGTKEbdu28c033+D1ernqqqvo2rVrWxf5tNTX1zNr1ixKSkro0qULd911V8zXORAIMHPmTL755huGDBnCjTfeGPN1DtqxYwfz5s3TxfsMMHHiRGpra0lLSyM3NzeqdY7JFv+ZXNC9rZSVlREIBEJLsv3rX/+id+/ejB07lhkzZlBTU8M//vEPRo0axU9/+lNmzJjRxiU+fZs2beKOO+7gueeeY+fOnbz00ksxX+fKykomTJjAQw89hNfr1cX7DFBaWspnn32G2+3WTZ3vvPNOXn/9dZ5//vmo1zkmg7+4uJjU1FSgYUH3WJOVlUXnzp1Dt4N1NpvNGI1GVqxYQUVFBampqaSmprJz505cLlcblvj0DR48mKSkJOrq6ujRowe7du2K+Trb7XZqa2uZM2cOffv21cX7fODAAQ4fPsyAAQMAfXy2PR4Pr776KnfffTevv/46GzdujGqdY7Krp7HjLegeSxrXUVGUZrfHwuvgdDpZtWoVU6dOZcqUKaH7Y7nOJpOJe+65h6lTp+rifZ4/fz4Oh4OKigrKy8t1UWeTycTf/vY3vF4vjzzySNi2aNQ5Jlv8elzQPTc3l4qKCnw+Hz6fj0suuYT09HQqKiqorq6md+/eJCQktHUxT4vb7WbdunXk5+dTU1MDEPN1djqddOjQgdTUVFJSUujZs2fM1/nuu+/moYce4uqrr6Zbt266+GwbDAasVis2m43s7Oyov88xeQGXz+fjjTfeoGvXrlRVVXHzzTe3dZFanc/no7CwkPfff5+HHnqIzp07895775Genk7Xrl25+OKL2bp1K2vWrCEQCDBy5Ei6devW1sU+LfPnz+ftt98O3b777rvZvn17TNf5gw8+oKysjAEDBuDz+bjwwgtj/n0OWrZsGcuWLeO+++6L+ToXFRWxe/duLrroIhwOB7m5uVGtc0wGvxBCiJbFZFePEEKIlknwCyGEzkjwCyGEzkjwCyGEzkjwCyGEzkjwC3EaHnjgAVavXh3RYzdu3Mgtt9zCe++9F+VSCXF8Evwi5vl8PkpLS0/qObt3747ocZdccknEk2Wdf/75oalEhGhLEvwipvl8Pl555ZWIgxy0uWKeffbZiB57ww03kJWVBYDL5WLPnj2nUkxAm4kzeFlNIBAAaPdTEYizU8zP1SP0benSpXz55ZccOXKEvXv34na7SU9PZ8uWLYwdO5Zu3boxa9Ysunfvzp49e7jvvvt49dVXKS8v55VXXmHgwIEMHjy42X3v2bOHBQsWUFBQQHx8PP/+97/p3bs3zz//PD6fj0ceeYTOnTuzcuVKPv74Y7p168bRo0dDz1+zZg1r1qzBZDJhtVoZPXo006dPZ+/evUybNo1Zs2Zx+eWXc9VVV52pl0vohLT4RUwbOXIkAPn5+WRlZbFq1SpMJhPJyckUFxezbt06duzYQa9evRg1ahTx8fEMGzYMgLvuuqvF0AetO+irr74CwGKxsG3bNvx+P9OnT8fpdLJmzRrKy8t58cUXGTNmDHfddRfx8fEA1NXV8cILL2CxWIiLi2Pv3r3Ex8fzu9/9DovFwocffsgVV1whoS+iQlr8Qjf27NlDcnIy1113Xei+6upqvvrqK6ZPn47NZuOJJ56IeH/BaYOB0LwpPXr0IC4uDqvVitvtZteuXfh8PjIzMwGIi4sDtO4kt9vN5ZdfTt++fUP7SUpK4pprrmHevHlcccUVp1NdIVokLX4R84xGIxUVFdhsNg4cOMCSJUuorq6muLiY3bt387vf/Y6ZM2diNBopLS3FZNLaQ+Xl5aFZXk9VcnIyADt37kRVVfx+PwAZGRmYTCbmz59PZWUlW7dupba2lrq6OsxmMwMGDOCVV17B6XSeXuWFaIYEv4h5Q4cO5YMPPsDtdjNkyBBef/11nnzySWw2GwkJCfz973/no48+4rzzzuP888+nb9++dOjQgccee4yKiooW97tixQoA1q9fz9q1awHYsGEDu3fvpra2lh07dpCdnc1ll13Gm2++yauvvkogEGDHjh14PB4mTZrE7t27efDBB/n+++9xuVw8++yzpKamMnToUI4cOcKLL76I1+s9I6+T0A+ZnVOIUxQIBDAYDKH/R8Ln84V+URzL7/ejKEpofwaDAVVVm12IQ4jTIcEvxHFs376dadOmNbnfbrdHPORTiLONBL8Qx+H1ekOrfTVmNBrlYizRbknwCyGEzsjJXSGE0BkJfiGE0BkJfiGE0BkJfiGE0BkJfiGE0Jn/D8TbhnQlp7/PAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 模拟抛硬币正面的概率是否会越来越接近0.5\n",
    "import random\n",
    "def Simulate_coin(test_num):\n",
    "    random.seed(100)\n",
    "    coin_list = [1 if (random.random()>=0.5) else 0  for i in range(test_num)]   # 模拟试验结果\n",
    "    coin_frequence = np.cumsum(coin_list) / (np.arange(len(coin_list))+1)  # 计算正面为1的频率\n",
    "    plt.figure(figsize=(6,4))\n",
    "    plt.plot(np.arange(len(coin_list))+1, coin_frequence, c='blue', alpha=0.7)\n",
    "    plt.axhline(0.5,linestyle='--',c='red',alpha=0.5)\n",
    "    plt.xlabel(\"test_index\")\n",
    "    plt.ylabel(\"frequence\")\n",
    "    plt.title(str(test_num)+\" times\")\n",
    "    plt.show()\n",
    "\n",
    "Simulate_coin(test_num = 500)\n",
    "Simulate_coin(test_num = 1000)\n",
    "Simulate_coin(test_num = 5000)\n",
    "Simulate_coin(test_num = 10000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e85aba89",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "下面，我们使用准确的数学语言总结以上的案例：对任意给定的 $\\varepsilon>0$， 事件 $\\left\\{\\left|v_{n}-p\\right| \\geqslant \\varepsilon\\right\\}$ 出现了就认为大偏差发生了。而大偏差发生的可能性越来越小，相当于\n",
    "$$\n",
    "P\\left(\\left|v_{n}-p\\right| \\geqslant \\varepsilon\\right) \\rightarrow 0,(n \\rightarrow \\infty) \n",
    "$$\n",
    "这时就可称频率序列 $\\left\\{v_{n}\\right\\}$ 依概率收敛。 这就是 “频率稳定于概率” 的含义。\n",
    "\n",
    "有了以上的案例铺垫，以概率收敛就很好理解了，具体来说：\n",
    "\n",
    "设 $\\left\\{X_{n}\\right\\}$ 为一随机变量序列， $X$ 为一随机变量， 如果对任意的 $\\varepsilon>0$， 有\n",
    "$$\n",
    "P\\left(\\left|X_{n}-X\\right| \\geqslant \\varepsilon\\right) \\rightarrow 0(n \\rightarrow \\infty),\n",
    "$$\n",
    "则称序列 $\\left\\{X_{n}\\right\\}$ 依概率收敛于 $X$， 记作 $X_{n} \\stackrel{P}{\\longrightarrow} X$。\n",
    "\n",
    "依概率收玫的含义是： $X_{n}$ 对 $X$ 的绝对偏差不小于任一给定量的可能性将随着 $n$增大而愈来愈小。或者说， 绝对偏差 $\\left|X_{n}-X\\right|$ 小于任一给定量的可能性将随着 $n$ 增大而愈来愈接近于 1 , 即$P\\left(\\left|X_{n}-X\\right| \\geqslant \\varepsilon\\right) \\rightarrow 0(n \\rightarrow \\infty)$等价于\n",
    "$$\n",
    "P\\left(\\left|X_{n}-X\\right|<\\varepsilon\\right) \\rightarrow 1 \\quad(n \\rightarrow \\infty) \n",
    "$$\n",
    "特别当 $X$ 为退化分布时， 即 $P(X=c)=1$（像概率p就是一个案例，频率不断趋近于一个常数p，这个p就是概率）， 则称序列 $\\left\\{X_{n}\\right\\}$ 依概率收敛于 $c$， 即 $X_{n} \\stackrel{P}{\\longrightarrow} c$。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "987457f5",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
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   "source": [
    "（2）依分布收敛：\n",
    "\n",
    "刚刚给大家介绍的依概率收敛，描述的是当$n \\rightarrow \\infty$时，随机变量序列越来越接近（趋近于）某个确定的随机变量的概率接近于1。同时，我们也知道随机变量的分布函数全面描述了随机变量的规律，因此会不会随机变量的分布函数序列$\\{F_n(x) \\}$会收敛到一个极限分布函数$F(x)$呢？而依分布收敛描述的就是随机变量的分布函数序列$\\{F_n(x) \\}$如何收敛到极限分布函数$F(x)$的规律，具体来说：\n",
    "\n",
    "设随机变量 $X, X_{1}, X_{2}, \\cdots$ 的分布函数分别为 $F(x), F_{1}(x), F_{2}(x), \\cdots$。 若对 $F(x)$ 的任一**连续点** $x$， 都有\n",
    "$$\n",
    "\\lim _{n \\rightarrow \\infty} F_{n}(x)=F(x),\n",
    "$$\n",
    "则称 $\\left\\{F_{n}(x)\\right\\}$ **弱收敛**于 $F(x)$， 记作\n",
    "$$\n",
    "F_{n}(x) \\stackrel{W}{\\longrightarrow} F(x) \n",
    "$$\n",
    "也称相应的随机变量序列 $\\left\\{X_{n}\\right\\}$ 按分布收敛于 $X$， 记作\n",
    "$$\n",
    "X_{n} \\stackrel{L}{\\longrightarrow} X \n",
    "$$\n",
    "\n",
    "在以上的定义中，我们看到一个词，叫弱收敛，为什么叫弱收敛呢？事实上，依概率收敛是一种比按分布收敛更强的收敛性，也就是说依概率收敛可以推出按分布收敛。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb7961e4",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
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   },
   "source": [
    "### 8.大数定律"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1813932d",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
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   "source": [
    "大数定律由雅各布·伯努利（1654－1705）提出，他是瑞士数学家、也是概率论的重要奠基人，伯努利大数定理以严密的数学形式论证了频率的稳定性。大数定律讲的是：当随机事件发生的次数足够多时，随机事件发生的频率$v_n$趋近于预期的概率$p$。可以简单理解为样本数量越多，频率越接近于期望值（概率值），这个解释是不是很像依概率收敛的概念，其实大数定律的确是依概率收敛的案例。大数定律的条件：独立重复事件与重复次数足够多。\n",
    "\n",
    "与“大数定律”对应的，就是“小数定律”， 小数定律讲的是：如果试验次数比较小，那么在试验中什么样的极端情况都有可能出现。当我们在判断随机事件发生的概率时，往往会违背大数定律，而不经意地使用“小数定律”，会觉得典型事件肯定会发生，往往会犯以偏概全的错误。黑天鹅事件往往就是指这种情况，即便一个东西概率很低，只要次数足够多，就一定会发生（金融危机），而如果这个东西会造成巨大的影响，我们不得不事先做好准备，避免遭受无法承受的打击。换句话来说，我们也会认为在单次试验中，小概率事件往往不发生，这个结论是假设检验的根本！\n",
    "\n",
    "下面，我们来介绍大数定律的两种表达，这两种表达都对后面的数理统计有十分重要的作用。\n",
    "\n",
    "- 伯努利大数定律：\n",
    "\n",
    "设 $S_{n}$ 为 $n$ 重伯努利试验（结果只有0-1）中事件 $A$ 发生的次数，$\\frac{S_{n}}{n}$就是事件 $A$ 发生的频率， $p$ 为每次试验中 $A$ 出现的概率， 则对任意的 $\\varepsilon>0$， 有\n",
    "$$\n",
    "\\lim _{n \\rightarrow \\infty} P\\left(\\left|\\frac{S_{n}}{n}-p\\right|<\\varepsilon\\right)=1 \n",
    "$$\n",
    "伯努利大数定律的道理是频率稳定于概率，已经在依概率收敛里讲的很清楚了，这里不多加阐述。下面，我们利用这个结论，看看如何使用伯努利大数定律计算定积分的值，这个方法叫做蒙特卡洛模拟法（随机投点法）。\n",
    "\n",
    "【例子】使用蒙特卡洛求定积分\n",
    "\n",
    "设 $0 \\leqslant f(x) \\leqslant 1$, 求 $f(x)$ 在 区间 $[0,1]$ 上的积分值\n",
    "$$\n",
    "J=\\int_{0}^{1} f(x) \\mathrm{d} x \n",
    "$$\n",
    "方法就是：我们在正方形$\\{0 \\leqslant x \\leqslant 1,0 \\leqslant y \\leqslant 1\\}$内均匀地投点$(x_i,y_i)$，投n个点，点越多越好。如果某个点$y_i \\le f(x_i)$,则认为事件发生，我们计算满足$y_i \\le f(x_i)$点的个数$S_n$，使用大数定律：频率稳定于概率，即：$\\frac{S_n}{n}$就是积分值。"
   ]
  },
  {
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   "execution_count": 119,
   "id": "490bd0d8",
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
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   "outputs": [
    {
     "data": {
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Nyq5TefBZupgzGC5ILX/QtAz+UsUiQkfR5oNL/SzJJq760TL4g1SxiHApm1u/NIBz8EBNgderNFKtn6UrFpzLmRL460S74K9i3lSIhZTLrXOxD/fMSWBxqaB6p5HGLTg1aUq/njrSKvjX+w9eiJqVyq3fsAxy2bnPq5AKmj3xITUEly9V/VovTVoOJydjmtaZq0Or4K9q3jRocvUTPqVy6+6lQTjTc91zS6WI5k98yvG73Dlvw8nLeQyQ3bt1plXwl/p+ufoJs/m5defgAdwSwb9kmWWpiU8JfpY7W1N34mpc7krgV4BWV17V9g+PNNndHB2LaLxX1QTHx3Jn24VPMiaWa2BK5FeCVjN/qe+P9tWPbumsxZRZll0wvnktJG7x9ffluHAyY5KTWzAqZcnB37ZtYrGYF2Px3WJrkqMYTKK6u1nXdFbVZZZlJj5+3xXMdYtVPZNyC0bl1Bz8bdvm7bffZv369dx5551ejslX1X5YIhtMonr1I4v5FdVjY6PrwumswbiNpHoUVDH4W5bFoUOHWLt2LWNjY+zYsWPmay+//DIdHR1s3rzZ90HWRUSDSVR3N0c5neWVIDc2ui6cyxmkCwYx2cSlpIrBv7u7m/HxcXbv3s3evXtJJpNs2rSJZDJJOp2ObuAn2sEkirubo5rOCqsLOYOU9OtRWsVqn2QyyapVqwBoaWnh2LFjAHz00UfcfvvtvPfee+zdu5d0Ou33OAMnlUEhI7ecVMbFnMFQwSAuqR6lVZ3zNwwD1y3OrbLZLC0tLWzZsoUPP/yQX/ziFzzwwAPXvaarq4uuri4A9u/fTyKRqG2Q8XjNr62VtfsJ0mdPYQ/1zzwWu2U9q3Y/QTyAsdTjmOttScecSGC98A9MvP4K9kiK2OoEKx76GvHWNm8H6bGovc8XJixGrQLNK8oHftM0aWpaHuCovBMfHmD1j/+JWPoy9qqbGfnyw1hr1lV8Tcx2icVirFbsfa4Y/Nvb2+npKW4iSafT3HHHHWQyGTZs2MDZs2eB4sLv9NXBfJ2dnXR2ds78O5VK1TTIRCJR82trFm/E+fpejFm5cWf7TtLxRghgLHU55hp4WRG15GOON8Kux4vjAtIQyHu1FGF5n6sxnDc4ly2megoVntfUtJxMZjKwcXmlITXIrT98lhsuX1sLbPz0Y8488mLFG8/kHbDtRlLp0Zp+blubPxOYisG/o6OD8+fPc+TIETZu3Ehvby/Nzc1s3bqVV199lZ///Oe0tLRw9913+zK4elMpN65i2WlkK6LEol3OFxd4o5zjv+Wd1+YEfoAbLg9yyzuvcWHXN+s0qtpVDP7xeJw9e/aU/NoTTzwBFE8Qwl/KBtmIVkSJxRktwJmcGfkcf8NY6WKPco+rTq8dvlVSbpataJCNckWUqM4VC05nox/4AQrNpYs9yj2uOgn+86g4y1Y1yEp5pd7GLDiVMbWp4x/atoumc5/MSf3kbm5laNuuOo6qdlo1dquKgo3PlC07lfJKbV214OSkqdXO3UKilTOPvMjo5q2Mf3YTo5u3LrjYqzKZ+c+j5Cxb0ZYMUd0tLCobt6B3MkYM/XryFxKtoVzcLUWr4F9NLl/FVIbfQXYpaxwqVUQJ/01Y0DN1Fy7dAn/UaBP8q87lKzzL9iPIqrjGIdQ0YUvgjxJ9cv5V5vLNqTa3xp1b4HPtGHdu8b3tbV0puMYh1DNhQ08mJrdfjBBtZv6LyeXrlMpQco1DKCUjgT+StAn+KubyVRDF34ty+zRCLGPDJxEO/A2p4g7dhrERCs2rGdq2K7TVO4ulTfBXNZdfdxH7vcgahneinuppSA3ymXm9elac/pjJ9X9ALDcZ+ZOBNsE/qLJEr2ad1uBFnH/+ge+z18iVayq6Gzpsoh74oXSvnsb0MI3p4Zl/N537JNS1/JVoE/zB/1y+V7NOZ3iQ9Pf34U61k17K7LWak1GU1jhkDWPppss5oxz4obqePGFu3LYQfap9guBV5czbP5pzH4Fav8/0ycj91XvQcxz3V+/hfu+54gkhopTdDR0S4xZ8okHgh+p78oS1cdtCJPh7yKtZp2ezVx3LOANsOeEMD+IcPID90rM4Bw+E/qRabNmgTx3/0LZd5G5e+Eo6rI3bFqJV2meaX9UgXlXOePV9dEyBBLm2E6WF5TELeidNbQI/XOvVM13tY9+wnGUXPuWGK9durhPmxm0L0S74+/qh9apyZvtOYvNuIVnL94liGWc1FlrD8OTkH6GF5StT3TlNw9Am8E+b36tHp9JP7YK/nx9ar2ad5ppWVj3/fUaWWu0TsTJOL3h18o/KVdVoodiPX5e2zAuJUuO2hWgX/P3+0HpVORNvbcNU5GQUKR6d/KNwVXU5r8cduERp2gX/KHxoFyNKZZxe8OzkH/BVldfrVJfyBn05QwK/xrQL/pIK0ZtXJ/8gr6q8XqcazBtcyEb7ZutiYdoFf0mFaM7Dk39gV1UerlP15wwG8hL4hYbBHyQVojMvT/5BNZDzIlXlunA+Z3CpIKkeUaRl8Bd68+LkH2Sd/1JTVa4LZ7MGI5YEfnGN7PAVohZB7p5ewq5l14VTkwYjBYOYBH4xi8z8haiBlyXDC6WPak1VOS6czJhMOEgdv7iOBH8hauBV1ZA1eLGq9NFiU1W2C59kTHIOMuMXJUnaR3giak3OFuRRA7mJ11/xPH1UcODjCZOcY2BK4BdlyMxfLFnUmpxVw6uqIXskVfLxWnecZ+3ijN/BQDI9ohIJ/mLpQtbkzKsSTS+qhmKrExRKPF7LjvPxqZbMBkjgFwuS4B8yKt6cPExNzlS7Slnx0NfInkguedPZFQtOadaSWSyNBP8QUS1wTQtVvyTFrlLirW0YS0wfDecNzkmfHrFIEvzDRLHANSNE/ZJUvEpZSvqoP2cwmJN2DWLxJPiHiIqBC8LVLylUVykVuC6czRlcLkjgF7WR4B8iKgeu0PRLCtFVSjmOW7zl4riNpHpEzSoGf8uyOHToEGvXrmVsbIwdO3bM+XpPTw+HDx/mO9/5jq+DFFNCELhUXJCeLUxXKaVYU5u38rJ5SyxRxeDf3d3N+Pg4u3fvZu/evSSTSTZt2gRAX18f7777LrlcLpCBCvUDl6oL0vOF5iplnqwNn0yaOK7U8Iulq7jDN5lMsmrVKgBaWlo4duwYAAMDA1y6dInPf/7zvg9QzGWuacXc8zSxb7yIuedppYJqoM3ONDNmwe8yMVwJ/MIjVef8DcPAdYsZ5zfffJPx8XEuX75MKpWiq6uLzs7O617T1dVFV1cXAPv37yeRSNQ2yHi85teGVRiPeWTiaskNS/GJq6yu4ljCeMxLNX3M1uBFJl5/BXskRWx1ghUPfY14axsAgxmLC2MWK5pcjAikekzTpKlpeb2HEZiY7RKLxar6DASpYvBvb2+np6cHgHQ6zR133EEmk+HRRx8F4OjRoxw9erRk4Afo7Oyc87VUqvRW9oUkEomaX1uK6nlp8P6Yg+CsuLHk49aKG6s6lmqOOQzv3WIkEgkunfiPOemyAhQ3fv31Cww0r2Mob0SqK2dT03Iymcl6DyMweQdsu5FUerSm17e1tXk8oqKKwb+jo4Pz589z5MgRNm7cSG9vL83Nzdx1112+DCYIYclLh5LPC9KRfe/KpMuuHv4RQzu/GXjgb0gNcss7r9EwNkKheTVD23ZRSIT49ytKqhj84/E4e/bsKfv1rVu3snXrVq/H5C9VN0pFgO8L0hF978ru07gyGnhFT0NqkM/88FluuHzt99x07hPOPPKinAAiJpR1/ku59Fd1o1RU+FlJ4+d7V890Urn9G1Zz8Ps3bnnntTmBH+CGy8UrgQu7vhn4eIR/Qhf8l3rpr/JGKVGZX+9dyb+pkx9jb/gDyE76fzIokS7L3dzK0LZd/vy8ChrGSp9Iyz0uwit0wX/Jl/4h2CglyvDrvSv1NzWaKv4P/9cWjEQrlx7738R+fIjGsdG65tkLZa42yj0uwit0wX+pl/6qb5QS5fn13lX1t+PT2oLjupzOGow2ryO+61uefu9aDG3bRdO5T+akfup1FSL8Fbrg78Wlf1h3eAp/3rtyf1Pzeb0uVHDhN5fzpC112jEXEq2ceeRFqfbRQOiCv6Rt5qp2oTJq9fGeKvU3VYKX60LjVrE52/ImR7kePYVEqyzuaiB0wV/SNtdUu/gd2fp4j8z/m2LZcjh/BkaGrz3JwwnGpbzB+ZyBidxgXdRP6II/SNpmRrWL3xGtj/fS/L8pP66U5vTgl6Av6iyUwV8UVbv4LXsbFs/rCYblQk/GJOeo0YNfdvEKCf4hVu3it+xtqK/p/L6LGh05ZRevgAVaOgvFbd9ZzEXPVio3Xe3zfOYMD+IcPID90rM4Bw8UUysRN5g3+GTSBEUCP1TexSv0ITN/hS2Ud6528VuFRXLdFp0dF85kDaXKOKfJLl4BEvyVZQ1erCpYVpubrvsiuUaLzjkbTmZNCorealHHXbyyxnE9SfsoauL1VyJ1VyxdFp1HCvAfmRiWo24Z59C2XeRunhv4oryLd3qN46bfHGXlqSQ3/eYon/nhszSkop92rERm/oqyR0rf1ETVYLlQiirqi86uC305g1TeIKb4lEq3XbzSqbQ0Cf6Kiq1OlLwl4mKDZRA7e6vK50d4Z3beht6sSdYhNHfc0mkXr6xxlCbBX1ErHvpa8VZ+SwiWgS2yVpHPV2HR2Q+jBTiTjWEAsXDEfe3ouMZRDQn+ioq3tmEsNVgGtMhabT6/7ovOHppO8wznDeKKp3l0J51KS5Pgr7ClBsugFlmjns+fLzeV5sk5EA9Jmkdnuq1xVEuCf4QFFpQjnM+f73IezuZimEiaJ0xmr3EEVfY5/XNiV0awWm+B//YVpdKcEvyjLKCgHNV8/mzTm7ZGLYO4BP3AeB2og2ptMf/nuJ8CJ48rtalRgn+EBRmUo5TPn2/ChlOTJrarRlM2XfgRqIMq+yz1c1Tb1CjBP+KiHJT95rowkDe4mDeIKdSbRxd+BOqgyj7LfT+V9ulI8BeihIJT7MQ5acuibr34EaiDKvss9/1UKoKQIjUh5knl4fhEjKxjhGbTVhT5EaiDam1R6ueoVgQhM38hptgunJ40uGLLoq4K/KjPD6rsc/bPiY2N0HKLetU+huu6paoBfXHx4sWaXpdIJEilSve6iSo55mBdseDMpIkTcG6/qWk5mcxkcD9QAYs55ih048w7cNf6ZpyrozW9vq2tzeMRFcnMX2jNceFs1mCkYBAzZFFXNTr1IAqaBH8RiCAazC3WmAVnslMlnBL1hWYk+AvfqXYXL8eFC/1DLP9/h7htbDS06QQhlkKCv/CfQnfxGrPgwoVL3PbD78oNzIXWJPgL36lwFy/bhXNTuf3b3jmk3M09orCwKcJFgr/wXb27fo4W4FzWxKbYflm1m3sE1W9GiNlkk5fw3/adxQ0uswWw4aXgQm/G5NOsCYYx04VTtZt7VGpjIIRfZOYvfFepwdzsKqArt6zDue+vlrwI7LowXDC4kCvObeZv2FLt5h6qXYkIPVQM/pZlcejQIdauXcvY2Bg7duwAYHJykldffZXe3l7a2tp4+umnaWxsDGTAIpxKNZibXwWU7TkOJ5JLqgLK2nA6azLplO+3r9rNPVS7EhF6qJj26e7uZnx8nPvvv58TJ06QTCYBOH78OA8//DAHDhzg5MmT9Pf3BzJYETGVqoAWyXGhL2vwccYk5xQ3bFUyvXnozGN/x4Vd36xrbj2ofjNCzFZx5p9MJmltLf5RtrS0cOzYMTZt2sQXv/hFAEZHR7ntttvYsGFDydd3dXXR1dUFwP79+0kkErUNMh6v+bVhpcMxj0xcpVDi8fjEVVYv4thTWZtPxwpYcbgxZBegpmnSsOEzDD51gNU//idiVy5jt9zMyJcfpmHNOhrqPUAfmKZJU9Pyeg8jMDHbJRaLLepvOghV5/wNw2B2G6BMJsMvf/lLnnnmGYwys6zOzk46Oztn/l1r3xbpcxNNzoobSz5urbixqmPP2XA2ZzJmQxyDMN5nZabPzYpVjD30v+Z+MaI9f3TrZ5R3wLYbSaXV6u1TMe3T3t7OyEhx0SmdTtPa2komkyGXy/HrX/+ae++9l7GxMbq7u30ZnB+c4UGcgwewX3oW5+CB4oKjqI8aq4AcFy5kDf4jYzJhGzQY4Qz8QtRTxZl/R0cH58+f58iRI2zcuJHe3l6am5sZGBjg9ddfn3ne448/7vtAvaBamwHdza8CWnbLOnILVPuMFOB8zsRyWTCvL4QoT6uWzs7BA7i/eu+6x407t2AqdqvDsKd9amnkVumYs3axCduEE6376OqWAgH9jllaOisg6DYDKnayDIKXV1j2VBXPZat4H125yYoQ3tAq+AfZZkDrFJMHjdymb54+mDdxuX6jVi2kf44Q1+jV3iHINgMe1rCHzVKusFy3mNc/PmEykC/eXKXcZq3FmO6fc9NvjrLyVJKbfnOUz/zwWRpSsuAv9KRV8DfXtGI89QLGnVvgc+0Yd27B8GkmrkIny3opdyW10BXWWN7mdxmT09ni7RS9XNCV/jlCzKVV2gdKtxnwQ707WdbV9p1wumfulU+FK6ysDedyJlYhT97xJ68v/XOEmEu74B+YRQbAKKnUyG22ggN9OYO0ZWBisGKZQcGnBV3pnyPEXBL8fVJtAIyq2VdY01VP9tTvwfnyTi40r+NywcDgWqvl+PAAtx5+1ZcFWdU6eQpRbxL8fRRUikllpaqe8qd6uPo/XyQ260TYkBqk7ZXv0jB8bS+Ilzc0Ua2TpxD1JsFf+KtE1dMNlwdZd2TuLRNveee1OYF/+nle3lpxupOnEEKzah8RLNuF7Eh1C62yICtEsGTmLzxnu9CfM7hcMLn1xpu5ocRz5i+0yoKsEMHSPvjr2oLBD4WpoD9SKO7KjRlwadsuVlSx0Dq0bRcrz5+ck/qRBVkh/KN18Ne6BYOHcjZcyBdLNg2Ku3KnVbvQWki0cvHrf0+zT9U+Qoi5tA7+XvSg0dm4Bf15k6s2mLNKNuerdqHVWrNOFmSFCIjWwV/nFgy1cl1IWzCQN8nYxZ76Ye60Kc3ehK60Dv5at2BYJMeFobzBcMEg71JsrxzyWrHpZm+z1yO83FsghMpC/vFdoiC7fIZU3oEzWYNj4zEu5g0cDOIRuW2iNHsTOtN65q97C4ZyXBeuWDBQMJmYyuebRnG2HyVh2lsg6SnhNa2DP0gLhtksFwbzBiOzUzvRivdzhGVvgaSnhB9CEfytwYs4//wDmZ37wHXhql1cwB23gamqnSgH/WlhafZWKT0l1VGiVsoHf2d4kPT39+EO9QNSi++VglO8TWLaMsi5EK9QqhlVYWn2Fqb0lNck3eUf5YM/b/8Ieyrwz5Ba/Jo4LoxYBsN5gwmHmXbKDZoF/dnC0OwtLOkpr0m6y1/KV/tILf7SuC6MWdA7afLReIyzkwZZp1ixo9tMP6yGtu0id/PcYKdiesprUo3lL+Vn/lKLv3iuCxkbLhUMrtgGham0jmmAGYUaTc2EJT3lNZ3TXUFQPvizfSexs6fmpn6kFv86rguTNlyyDMYsg5zDTD3+/LSO5FHDJwzpKa/pmu4KivLB31zTyqrnv8+IVPtcZ/YM/6ptkHeKM3vTgIYyCT3Jo4qwCEs1VlgpH/wB4q1tmLK4CxQXbccsGLYMMnaxHj9OcYZfTbsFKRsU86l6JahruisooQj+uss7MFIwSNvFgG+7btmUzkIkjypmU/1KUMd0V1CUr/bRkePCSM7m00mD4+MmyQmTC3mTrDOd0qm9t47kUcVsUlGjLwn+CnBdmLCgL2vwuwmTj8ZNkqMFxiwTe6qRmlc7bkuVDdqNy2i8PMCtr/09DanBMq8UUSRXgvqStE8dOFMLtSOWwYRtMOkY2LjEZsoxodEEy4eqzNl51MbUAMsGzxHLZ1lxrocV53qUuuQX/pMrQX3JzD8AeQcuF+DTSYOPp2b2JyZNUgWTnDuVyjHm3v7QT9N51HxiHbF8ds7X5JJfL7puIBMy8/dcwYEJG65MzehzTvHG5rjFu14ZUzN7Fc66cskvpKJGXxL8a+S4kHPgqm1w1Ya8U2yQZrnFHH5s1kw+boCKrfDlkl+AVNToqmLwtyyLQ4cOsXbtWsbGxtixY0fFx6PGdYuz9pwD47ZBxoGCU6ytL7jgMNUcDWaqb1QN9KXIJhoh9FUx+9Dd3c34+Dj3338/J06cIJlMVnw8bGwXsk5x09RQ3uBc1qB30uTEhMnxcZPfjsdITpicyJhczJuMWSZZt3grw5hh0DBVhRPWdjnTl/yjm7cy/tlNjG7eKou9Qmii4sw/mUzS2loMBC0tLRw7doxNmzaVfTwI7lSXt6k0Oo479f9T/+1QzLtbbrGhWWEqFWO7Bo5bDPg2xa+7rosz9X1MY+4MHqZz80ZoZvK1kEt+IfRUdc7fMIrBstrHAbq6uujq6gJg//79tLW11ThMlvTa8Gqu9wDqQI5ZDxoe843L6z2COSqmfdrb2xkZKVZ+pNNpWltbyWQy1z3e3t5e8vWdnZ3s37+f/fv3L2mQ3/72t5f0+jCSY9aDHLMeVDzmisG/o6ODpqYmjhw5wsaNG+nt7SWZTF73+Be+8IWgxiuEEMIDFdM+8XicPXv2lPxauceFEEKoT4W9Rgvq7Oys9xACJ8esBzlmPah4zIZbbrVWCCFEZIVi5i+EDmzbrvcQhEYk+AtRZ7Ztc/jwYT788MN6D0VoRLnePrq1lCh3XJOTk7z66qv09vbS1tbG008/TWNjY51H642F3suenh4OHz7Md77znTqN0HuVjvnll1+mo6ODzZs313GE3it3zKlUisOHD7NhwwYuXLjAV7/6VYywbpMv4fjx47zxxhvs27dv5jEV45dyM/+ot5SYr9xxHT9+nIcffpgDBw5w8uRJ+vv76zxS71R6L/v6+nj33XfJ5XJ1HKH3yh1zMpkknU5HLvBD+WN+//33ufXWW7nvvvsYHR1lYmKiziP1Tn9/P47jkEql5jyuYvxSLvgnk0lWrVoFXGsdUenxsCt3XF/84hdZuXIlExMT3HbbbWzYsKGOo/RWuWMeGBjg0qVLfP7zn6/j6PxR7pg/+ugjbr/9dt577z327t1LOp2u3yA9Vu6Y7777bvr6+kilUtxzzz2sXLmyjqP01vr161m3bt11j6sYv5QL/rPV0lIizOYfVyaT4Ze//CXPPPNMpC6LZ5t9zG+++Sbd3d288847nD9/fqY1SNTMPuZsNsuyZcvYsmULzc3N/OIXv6jz6Pwx/5i/9KUvsWzZMg4fPszgoF63DlUlfikX/JfaUiJsyh1vLpfj17/+Nffeey9jY2N0d3fXeaTeKXfMjz76KN/61rfYtm0bv/d7v6dkbXStyh3zhg0bGB0dBYoLv9Ozwygod8w/+9nPuHr1KitXrmTdunX09fXVeaT+6e/vVzZ+Kbfg29HRwfnz5+e0lGhubr7u8ai0lCh3vAMDA7z++uszz3v88cfrOEpvlTvmu+66q95D8025Y966dSuvvvoqP//5z2lpaeHuu++u91A9U+mYf/rTn5LNZmlubo7UeodlWXzwwQeMj4/z8ccfc/ToUf74j/9Yyfglm7yEEEJDyqV9hBBC+E+CvxBCaEiCvxBCaEiCvxBCaEiCvxBCaEiCvxBCaEiCvxBCaEiCvxBCaOj/A68+SB3LwXbjAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 蒙特卡洛积分计算的原理：\n",
    "x_arr = np.linspace(0,1,1000)\n",
    "x_n = uniform.rvs(size = 100)  # 随机选择n个x随机数\n",
    "y_n = uniform.rvs(size = 100)  # 随机选择n个y随机数\n",
    "plt.stackplot(x_arr,np.square(x_arr),alpha=0.5,color=\"skyblue\") #堆积面积图\n",
    "plt.scatter(x_n,y_n)\n",
    "plt.text(1.0,1.0,r'$y=x^2$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "637d0022",
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y=x**2在[0,1]的定积分为： 1/3\n",
      "模拟10次的定积分为： 0.3\n",
      "模拟100次的定积分为： 0.3\n",
      "模拟1000次的定积分为： 0.34\n",
      "模拟10000次的定积分为： 0.3302\n",
      "模拟100000次的定积分为： 0.33285\n",
      "模拟1000000次的定积分为： 0.333851\n"
     ]
    }
   ],
   "source": [
    "# 使用蒙特卡洛法计算y=x^2在【0，1】上的定积分\n",
    "from scipy.stats import uniform\n",
    "def MonteCarloRandom(n):\n",
    "    x_n = uniform.rvs(size = n)  # 随机选择n个x随机数\n",
    "    y_n = uniform.rvs(size = n)  # 随机选择n个y随机数\n",
    "    f_x = np.square(x_n)    # 函数值f_x = x**2\n",
    "    binory_y = [1.0 if y_n[i] < f_x[i] else 0 for i in range(n)]    # 如果y<x**2则为1，否则为0\n",
    "    J = np.sum(binory_y) / n\n",
    "    return J\n",
    "    \n",
    "print(\"y=x**2在[0,1]的定积分为：\",integrate(x**2, (x,0,1)))\n",
    "print(\"模拟10次的定积分为：\",MonteCarloRandom(10))\n",
    "print(\"模拟100次的定积分为：\",MonteCarloRandom(100))\n",
    "print(\"模拟1000次的定积分为：\",MonteCarloRandom(1000))\n",
    "print(\"模拟10000次的定积分为：\",MonteCarloRandom(10000))\n",
    "print(\"模拟100000次的定积分为：\",MonteCarloRandom(100000))\n",
    "print(\"模拟1000000次的定积分为：\",MonteCarloRandom(1000000))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40c4e656",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "- 辛钦大数定律：\n",
    "\n",
    "设 $\\left\\{X_{n}\\right\\}$ 为一**独立同分布**的随机变量序列， 若 $X_{i}$ 的数学期望存在， 则 $\\left\\{X_{n}\\right\\}$ 服从大数定律， 即对任意的 $\\varepsilon>0$，$\\lim _{n \\rightarrow \\infty} P\\left(\\left|\\frac{1}{n} \\sum_{i=1}^{n} X_{i}-\\frac{1}{n} \\sum_{i=1}^{n} E\\left(X_{i}\\right)\\right|<\\varepsilon\\right)=1$成立。\n",
    "\n",
    "对于独立同分布且具有相同均值 $\\mu$ 的随机变量X，$X_1, X_2, \\ldots \\ldots  X_n$ ，当 $n$ 很大时，它们的算术平均数 $\\frac{1}{n} \\sum_{i=1}^{n} X_{i}$ 很接近于 $\\mu$。也就是说可以使用样本的均值去估计总体均值（这里不明白没有关系，后面讲到数理统计的时候会重申这个概念）。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8590de24",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### 9.中心极限定理"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3e84863",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "大数定律讨论的是在什么条件下（独立同分布且数学期望存在），随机变量序列的算术平均**依概率收敛**到其均值的算术平均。下面，我们来讨论下什么情况下，独立随机变量的和$Y_n = \\sum_{i=1}^nX_i$的分布函数会依分布收敛于正态分布。我们使用一个小例子来说明什么是中心极限定理：\n",
    "\n",
    "我们想研究一个复杂工艺产生的产品误差的分布情况，诞生该产品的工艺中，有许多方面都能产生误差，如：每个流程中所需的生产设备的精度误差、材料实际成分与理论成分的差异带来的误差、工人当天的专注程度、测量误差等等。由于这些因素非常多，每个影响产品误差的因素对误差的影响都十分微笑，而且这些因素的出现也十分随机，数值有正有负。现在假设每一种因素都假设为一个随机变量$X_i$，先按照直觉假设$X_i$服从$N(0,\\sigma_i^2)$，零均值假设是十分合理的，因为这些因素的数值有正有负，假设每一个因素的随机变量的方差$\\sigma_i^2$是随机的。接下来，我们希望研究的是产品的误差$Y_{n}=X_{1}+X_{2}+\\cdots+X_{n}$，当n很大时是什么分布？"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "7b4e62e7",
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYYAAAEXCAYAAACpuuMDAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsTAAALEwEAmpwYAAAbNklEQVR4nO3df1TV9eHH8deFSwkTIbyZIQopHh1BLXcmNrTyxA7UmEdrFelqadEBdw7bKRdt7hzn6eTYnK1o/iBPtXZKz3GMpkcp23UxJTOZrWCJ4dEWimbci3RlEJfL/Xz/aPD1LahMufBRno9/9PN+3/u5r/uRy8vP+/K5OCzLsgQAwH+FDXUAAIC9UAwAAAPFAAAwUAwAAAPFAAAwUAwAAAPFAAAwUAzAALMsS88995yys7ONcZ/Ppx/84AdauHCh5s6dq/r6+p65/fv3KycnRwsXLtTChQvV2traM/f6668rJydHubm5WrFihbHPX/7yl7r33ns1Z84cbd26NbRPDMOHBWDA7N+/3yosLLSSk5OtW2+91ZjLzc21Hn30UcuyLOu1116zJk2aZPn9fqujo8OaMGGCtWHDBsuyLCsvL8964IEHLMuyrNraWuvKK6+0jhw5YnV1dVlTp061XnzxRcuyLGvdunXW1KlTra6uLuvIkSPWiBEjrLq6usF7srhsccaAYWfHjh0h27ff79czzzyjcePGGeOHDx/Wpk2bNGvWLEnSLbfcokOHDmnjxo3asGGDGhoajLkNGzbok08+0W9/+1slJCQoISFBYWFhysjI0NNPPy3LslRcXKyMjAyFhYUpISFB48aN029+85uQPTcMH86hDgAMloaGBq1cuVL/+te/tGfPHv36179WWlqatm7dqquuuqrX7YuLi/XBBx/0ua+kpCQVFxf3Gr/xxhv7vP3u3bsVDAY1ZswYSdLVV18tSdq1a5es/34qzelzXV1d2r17t6qqqnrGu+cOHz6shoYG/fvf/+41t2vXrn4cCeDcKAYMG4cPH9b69esVExOjwsJClZSUaOHChdq4caMWL17c6/ZPPvnkgD12Y2OjJMnp/Oold8UVV/SMdxdDX3ONjY2Kj4/v2U/33GeffWbcp3uu+3GAi0ExYNi47bbbNHbsWCUlJWnevHn65JNPJElNTU0hf+zub+5tbW2SvlpykqRx48YpGAz2zI0cOdKYi4+P77nP6fcbO3assb/uuTOXsIALQTFg2HI4HJLU8z/2Mz399NP65z//2efcddddp5UrV/b7sW6++WaFhYXp+PHjkv6/jGbOnKlgMKiXXnpJx48f1+TJk9XU1KSwsDDdfPPNmjlzptxud89+mpqadN1112nChAlKTEzs2V/3XPf7FMDFoBiAs1i6dOmA7Ss5OVm5ubnasWOH8vLyVFVVpYkTJ+r++++XJD311FPasWOHJk+erKqqKs2fP18TJ05UUVGRNm7cqAMHDmjKlCnavXu3li5dKofDoaVLl+qpp55SZ2enmpqadOzYMf30pz8dsMwYvigGDBuvvvqqTpw4oVOnTqmyslJvvPGGJKmiokIPPPCAJk2adNGP4fP59Oyzz+r9999XWFiYVqxYoSVLluiKK67QunXrlJ+frx/+8Ifyer3asWNHz3sGFRUVeuyxx/Tee++pq6tL69evlySlpKSorKxMP/nJTxQTE6MHH3xQDz/8sCQpLy9Pn332me677z51dHSovLxcKSkpF/0cAId1tvNo4DJjWVbP8hGAs+M6BgwblALQPxQDAMBAMQAADBQDAMBAMQAADBQDAMBw2VzHcOzYMWPb5XLJ4/EMUZrzs3s+yf4ZyXdxyHfx7J7xfPlO/xyu03HGAAAwUAwAAAPFAAAwUAwAAAPFAAAwUAwAAAPFAAAwUAwAAAPFAAAwXDZXPgPn0pU3Z9Af84Sk8PVbBv1xgYtFMQAhNBSF1I1SwoViKQkAYKAYAAAGigEAYKAYAAAGigEAYKAYAAAGigEAYKAYAAAGigEAYKAYAAAGigEAYKAYAAAGigEAYKAYAACGISkGy7K0a9euoXhoAMB5hPT3MbS3t2v9+vU6ePCg4uPjtWDBAi1ZskSSlJGRoVmzZqmurk7V1dXq7OxUVlaWEhISVFFRIb/fL4/HowULFigyMjKUMQEApwnpGUNtba0WLVqkVatWqb6+Xm1tbVq7dq1efvll5efnKxAIqKSkRNnZ2UpPT1dpaamOHj2qbdu2ae7cuYqOjtbmzZtDGREAcIaQnjFMnz5dknTy5EklJSWptbVVzz77rDo7O3XPPfcoJSVFXq9XsbGx8vv9qq+vV21trWJiYiRJsbGxqqysVG5ubq99u91uud1uSVJxcbFcLpf5xJzOXmN2Yvd8kv0z/i/5ToQ4ix2d79hcTv++Q8XuGS80X8h/tWdbW5v27NmjoqIiBYNBrVmzRocOHdKyZcu0YsUK47aWZcmyrJ5th8NhbJ8uMzNTmZmZPdsej8eYd7lcvcbsxO75JPtntHu+oXa+Y2P342f3fJL9M54vX3x8fJ/jIV1K6ujo0L59+zR79mz5fD7t3r1bYWFhmjx5slwulxISEhQXFyev16uWlhYlJycrLS1Nzc3NkqSWlhalpqaGMiIA4AwhPWOoqKjQxo0be7avueYatba2yuVyKT8/X06nU4WFhdq+fbuCwaAKCgo0fvx45eTkqLy8XD6fT/Pnzw9lRADAGUJaDPPmzdO8efPOeZuUlBSlpKQYYzk5OaGMBQA4By5wAwAYKAYAgIFiAAAYKAYAgIFiAAAYKAYAgIFiAAAYKAYAgIFiAAAYKAYAgIFiAAAYKAYAgIFiAAAYKAYAgIFiAAAYKAYAgIFiAAAYKAYAgIFiAAAYKAYAgIFiAAAYKAYAgIFiAAAYKAYAgIFiAAAYKAYAgIFiAAAYKAYAgIFiAAAYKAYAgIFiAAAYnKHceXt7u9avX6+DBw8qPj5e+fn5KisrU3R0tJKSkjRjxgzV1dWpurpanZ2dysrKUkJCgioqKuT3++XxeLRgwQJFRkaGMiYA4DQhPWOora3VokWLtGrVKtXX12vNmjVKTk7W3XffrdLSUvl8PpWUlCg7O1vp6ekqLS3V0aNHtW3bNs2dO1fR0dHavHlzKCMCAM4Q0jOG6dOnS5JOnjyppKQkHTp0SHfeeaciIiIUHh6uqqoqeb1excbGyu/3q76+XrW1tYqJiZEkxcbGqrKyUrm5ub327Xa75Xa7JUnFxcVyuVzmE3M6e43Zid3zSfbP+L/kOxHiLHZ0vmNzOf37DhW7Z7zQfCEtBklqa2vTnj17VFRUpIKCgp5xh8PR67aWZcmyLOM2p2+fLjMzU5mZmT3bHo/HmHe5XL3G7MTu+ST7Z7R7vqF2vmNj9+Nn93yS/TOeL198fHyf4yFdSuro6NC+ffs0e/Zs+Xw+SZLX61UgEFAgEFBGRobi4uLk9XrV0tKi5ORkpaWlqbm5WZLU0tKi1NTUUEYEAJwhpGcMFRUV2rhxY8/24sWLdeDAATU3NysvL08xMTEqLCzU9u3bFQwGVVBQoPHjxysnJ0fl5eXy+XyaP39+KCMCAM4Q0mKYN2+e5s2bZ4zddtttxnZKSopSUlKMsZycnFDGAgCcA9cxAAAMFAMAwEAxAAAMFAMAwEAxAAAMFAMAwEAxAAAMFAMAwEAxAAAMFAMAwEAxAAAMFAMAwEAxAAAMFAMAwEAxAAAMFAMAwEAxAAAMFAMAwEAxAAAMFAMAwEAxAAAMFAMAwEAxAAAMzqEOgOGlK2/OgO3rxIDtCcDpOGMAABgoBgCAgaUk4DJ1vmW7UC3Fha/fEqI9Y7D0uxgaGhr0+eefS5LGjBmjCRMmhCwUAGDonLcYKioqtG3bNjU3N2vkyJFyOBw6deqUrr76as2ZM0eZmZmDkRMAMEjOWgyBQEC///3vNXr0aD3++OOaMGGCnE5nz9ynn36q9957T+vWrdMjjzzSM9cflmWpqqpKs2bNuvhnAAAYUGf9br5v3z7l5uZq7Nixve/kdCoxMVGTJk2Sz+dTTU2Npk2b1ud+amtrVVZWpuXLl6uhoUFLliyRJGVkZGjWrFmqq6tTdXW1Ojs7lZWVpYSEBFVUVMjv98vj8WjBggWKjIwcoKcLADifs/5UUnp6ulEKb731Vs/f29vb9bvf/U6SNGrUqLOWQmNjo4LBoDweT8/91q5dq5dffln5+fkKBAIqKSlRdna20tPTVVpaqqNHj2rbtm2aO3euoqOjtXnz5gF5ogCA/un3+s/f//53hYeH65prrtHatWt7vtmfy7hx4xQREdGz3dbWpqVLl6qzs1P33HOPUlJS5PV6FRsbK7/fr/r6etXW1iomJkaSFBsbq8rKSuXm5vbat9vtltvtliQVFxfL5XKZT8zp7DVmJ3bPJ4UmIxelXf4G6mtmuL5GBtKF5utXMQSDQeXl5WnLli164YUXlJqaqnnz5v3PDzZlyhStWbNGhw4d0rJly7RixQpj3rIsWZbVs+1wOIzt02VmZhpvfJ9ZVC6Xq1/lNVTsnk+6NDLCfgbqa+ZS+Pqze8bz5YuPj+9zvF/FEBYWpqKiIo0YMUJ33XWXIiIiFBYWpq6uLoWHh/c7ZFRUlCRp8uTJcrlcSkhIUFxcnLxer1paWpScnKy0tDRt2fLVz0G3tLQoNTW13/sHAFy8fi8lJSUl6fHHH9eYMWPU1tamlStXavbs2ee8TyAQ0N69e9Xa2qqPPvpI77zzjsaMGSOXy6X8/Hw5nU4VFhZq+/btCgaDKigo0Pjx45WTk6Py8nL5fD7Nnz//op8kAKD/HNZZ1mr27t2rpKQkjRkzRpZlqbm5WaNHj+6Z93g8iouLU2trqw4dOqSbbrpp0EL35dixY8b2pX6KZwehyDiQH6IHexqoK5+H62tkIA34UtK0adO0evVquVwuZWRkGFc6d3V1yefz6a233lJra6sWLVp0EdEBAHZy1mJwOp368Y9/rIqKCq1cuVItLS2Kjo6WZVk6deqUXC6X5syZw1IPAFxmzvsew5133qk77rjD+Kyka665hs9KAoDLVL/efHY4HEpMTFRiYmKo8wAAhhi/jwEAYKAYAACGfl/H8OGHH+rll1/WyZMnNWXKFOXl5enqq68OZTYAwBDo9xnDunXrFBUVpdtvv10jRozQ2rVrQ5kLADBE+n3GMHbsWC1btqxne/Xq1T1/r6mp0Q033DCwyQAAQ6JfxXD06FGNGjVKlZWVcjgcam9vV1NTk3bu3CnLsvTWW29RDABwmehXMXzta1/TP/7xD+3Zs8cYr6urC0koAMDQ6VcxXHXVVfr5z3+u66+/vs/5t99+e0BDAQCGTr/ffD5bKUg676esAgAuHVzHAAAwUAwAAAPFAAAwUAwAAAPFAAAwUAwAAAPFAAAwUAwAAAPFAAAwUAwAAAPFAAAwUAwAAAPFAAAwUAwAAAPFAAAwUAwAAAPFAAAwUAwAAEO/fufzxaitrVVZWZmWL1+ukydPqqysTNHR0UpKStKMGTNUV1en6upqdXZ2KisrSwkJCaqoqJDf75fH49GCBQsUGRkZ6pgAgP8K6RlDY2OjgsGgPB6PJOmVV15RcnKy7r77bpWWlsrn86mkpETZ2dlKT09XaWmpjh49qm3btmnu3LmKjo7W5s2bQxkRAHCGkJ4xjBs3ThERET3bNTU1uvXWWxUREaHw8HBVVVXJ6/UqNjZWfr9f9fX1qq2tVUxMjCQpNjZWlZWVys3N7bVvt9stt9stSSouLpbL5TLmnU5nrzE7sXs+KTQZTwzo3mBHA/U1M1xfIwPpQvOFfCnpdJZl9fzd4XD0OX/mbU7fPl1mZqYyMzN7trvPSrq5XK5eY3Zi93zSpZER9jNQXzOXwtef3TOeL198fHyf44P65nNaWpq8Xq8CgYACgYAyMjIUFxcnr9erlpYWJScnKy0tTc3NzZKklpYWpaamDmZEABj2QnrGEAgEtHfvXrW2tuqjjz7SQw89pE2bNqm5uVl5eXmKiYlRYWGhtm/frmAwqIKCAo0fP145OTkqLy+Xz+fT/PnzQxkRAHAGh3W2tZpLzLFjx4ztS/0Uzw5CkbErb86A7g/2E75+y4DsZ7i+RgbSJbGUBACwP4oBAGCgGAAABooBAGCgGAAABooBAGCgGAAABooBAGCgGAAABooBAGCgGAAABooBAGCgGAAABooBAGCgGAAABooBAGCgGAAABooBAGCgGAAABooBAGCgGAAABooBAGCgGAAABooBAGCgGAAABooBAGCgGAAABooBAGCgGAAABudQPvjOnTt1yy23DGWEYakrb06/bncixDkA2NOQFMPDDz+sU6dO6aqrrlJaWprKysoUHR2tpKQkzZgxQ3V1daqurlZnZ6eysrKUkJAwFDEBYFgakmJ49NFHlZqaKofDoRdeeEE33nijZs6cqUcffVQpKSkqKSnR8uXL9fnnn6u0tFRPPfXUUMQEcAH6e0Z6Phdyxhq+fsuAPPZwN+jF4Pf79eKLL6qjo0PTp0/Xhx9+qFtvvVUREREKDw9XVVWVvF6vYmNj5ff7VV9fry+//FIjRoww9uN2u+V2uyVJxcXFcrlcxrzT6ew1ZidDmY8lIlyuBvs1dbl+nxn0YnA6nXr22WfV2dmpX/ziF8acw+HodXvLsmRZVq/xzMxMZWZm9mx7PB5j3uVy9RqzE7vnAy5Fg/2asvvr+Hz54uPj+xwf9J9KCgsLU1RUlGJiYpSYmKiJEyfK6/UqEAgoEAgoIyNDcXFx8nq9amlpUXJysiIjIwc7JgAMW4N+xuB2u3X48GF985vf1Le+9S2lpaVp06ZNam5uVl5enmJiYlRYWKjt27crGAyqoKBgsCMCwLA26MVw+vJPt/z8fGM7JSVFKSkpgxUJAHAaLnADABgoBgCAgWIAABgoBgCAgWIAABgoBgCAgWIAABgoBgCAgWIAABgoBgCAgWIAABgoBgCAgWIAABgoBgCAgWIAABgoBgCAgWIAABgoBgCAgWIAABgoBgCAgWIAABgoBgCAgWIAABgoBgCAwTnUAYazrrw5Qx0BAHqhGABcNgb7P1sn/vtn+Potg/q4ocZSEgDAQDEAAAwUAwDAQDEAAAwUAwDAYMufSgoEAnr11Vc1ZswY+Xw+5ebmDnUkABg2bFkMf/vb39Ta2qqHHnpIy5YtU01NjW644YaQPNZQXUtw4vw3AXCJGMprkkLxo7K2LIaamhqNHTtWkhQTE6MPP/ywVzG43W653W5JUnFxseLj43vtp6+xXrb94+IDA4BN9ev74Bls/x6Dw+GQZVm9xjMzM1VcXKzi4uI+7/fkk0+GOtpFsXs+yf4ZyXdxyHfx7J7xQvPZshjS0tLU3NwsSWppaVFaWtoQJwKA4cOWxXD77bcrKipKb775pqZOnaqbbrppqCMBwLBhy/cYnE6nHnnkkYvaR2Zm5gClCQ2755Psn5F8F4d8F8/uGS80n8PqawEfADBs2XIpCQAwdCgGAICBYgAAGGz55vOFOH78uJ5//nmtWLFC7e3teu211+RyuXTllVfqjjvu0NGjR7V9+3Y5nU6lp6dr6tSpg5Ztw4YN2rlzpxITE/Wzn/3MVvm6urr00ksvaf/+/YqKilJRUZEiIiJsk0+SDh8+rNWrV2vVqlWSZKvj1xc7fqRLbW2tysrKtHz5cp08eVJlZWWKjo5WUlKSZsyYobq6OlVXV6uzs1NZWVlKSEgYtGzt7e1av369Dh48qPj4eOXn59sqXzAY1AsvvKDq6mrNmDFD3//+922Vr9vHH3+s8vLyATl+l8UZg8fj0ZtvvqkvvvhCklReXq5Ro0Zp7ty52rp1q44dO6a1a9cqPT1d2dnZev7559XV1TUo2dra2pSVlaUVK1bI7/fbLl99fb2+973v6ZlnnlF7e7sOHDhgq3zd17McOXKkZ8xO+frS/ZEud955p+rq6lRTUzNkWSSpsbFRwWBQHo9HkvTKK68oOTlZd999t0pLS+Xz+VRSUqLs7Gylp6ertLR0UPPV1tZq0aJFWrVqlerr67VmzRpb5WtubtaDDz6oJ554Qp2dnbY7fpLU0NCgv/71r+ro6BiQfJd8MXzxxReqq6vT9OnTe8ZqamoUGxsrSRo1apQ++OADHTx4ULGxsYqNjVVTU5OOHTs2KPmioqIUERGhl156Sd/4xjfU1dVlq3xf//rXNXbsWPn9fo0cOVKpqam2yhcXF6eJEycaY3bK15fT83V/pMtQGjdunK699tqe7e58ERERCg8PV1VVlbxeb8/xq6+v15dffjlo+aZPn66RI0fqP//5j5KSknTo0CFb5XO5XDp16pTKyso0ZcoU2x2/48eP6/PPP1dqaqqkgfn3veSXkrZu3arGxkadOnVKX3zxhcrLy415h8PR5/Zg/pRuIBBQQUGBli9frujoaFvme/vtt/XYY49pxIgRtst3LpdCPrtk6XZ6njOPX/f8YGdua2vTnj17VFRUpIKCgp5xu+RzOp360Y9+pKKiItsdv9dff12tra3yer3yeDwDku+SLYb3339fDQ0NSkxM1IIFC/TRRx9pzZo1uuuuu9TW1iav1yvpqzOKtLQ0TZo0Sc3Nzbriiis0evToC/pgqQvJN3r0aGVkZCgsLEwul0tRUVFKS0uzTT6Xy6VAIKBbbrlFgUBAFRUVtss3c+ZMY84O+c4lLS1NH3/8saSvPtLltttuG7Isfek+foFAQIFAQBkZGdqyZYu8Xq9aWlqUnJysyMjIQcvT0dGhffv2afbs2fL5fJJkq3xtbW0aPXq0pK/OUEeNGmWrfIsXL5YkVVZWqrKyckDyXTYXuHUXw+rVq9XW1qY//vGPio+PV3h4uL773e/qyJEjeuONNxQZGalp06bp+uuvH5RcO3fu1LvvvqtZs2bJ4/Fozpw5tspXVVWlkpKSnu377rtPd9xxh23ySdI777yj5557TkuWLNH06dNtdfz6EggE9Ic//EEJCQk6efKk7r///iHL0p3nzTff1J/+9Cc98cQTuvbaa7Vp0ybFxcUpISFB3/72t7V//37t3btXwWBQ3/nOdzR+/PhBy/f6669r48aNPduLFy/WgQMHbJPvL3/5ixobG5WamqpAIKCbbrrJVsevW3cxFBYWXnS+y6YYAAAD45J/8xkAMLAoBgCAgWIAABgoBgCAgWIAABgoBgCAgWIAABgoBiBEgsFgz5/dlwtx2RAuBZfsR2IAdvfqq69q69atys3NVWdnpxobG/XQQw8pLi5uqKMB58SVz0AI/epXv9LRo0eVkZGhe++9V04n/xeD/bGUBITQwoUL1dTUJK/XSyngkkExACH07rvv6sEHH9SuXbtUXV091HGAfqEYgBAIBoP685//rI8//ljTpk1TVFSUSktL9emnnw51NOC8eI8BCJHOzk6FhYXJsqyeZSTLsvr85SmAnVAMAAADS0kAAAPFAAAwUAwAAAPFAAAwUAwAAAPFAAAwUAwAAMP/AV1eZUU3pLAjAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 模拟n个正态分布的和的分布\n",
    "from scipy.stats import norm\n",
    "def Random_Sum_F(n):\n",
    "    sample_nums = 10000\n",
    "    random_arr = np.zeros(sample_nums)\n",
    "    for i in range(n):\n",
    "        mu = 0\n",
    "        sigma2 = np.random.rand()\n",
    "        err_arr = norm.rvs(size=sample_nums)\n",
    "        random_arr += err_arr\n",
    "    plt.hist(random_arr)\n",
    "    plt.title(\"n = \"+str(n))\n",
    "    plt.xlabel(\"x\")\n",
    "    plt.ylabel(\"p (x)\")\n",
    "    plt.show()\n",
    "\n",
    "Random_Sum_F(2)\n",
    "Random_Sum_F(10)\n",
    "Random_Sum_F(100)\n",
    "Random_Sum_F(1000)\n",
    "Random_Sum_F(10000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "043a7995",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "有可能你会觉得，n个正态分布的和肯定还是正态分布啦，那如果误差满足其他分布的情况下，是否还有上述实验的规律呢？我们验证下，这次我们使用均匀分布、指数分布、泊松分布、0-1分布："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "0280901b",
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 模拟n个均匀分布的和的分布\n",
    "from scipy.stats import uniform\n",
    "def Random_Sum_F(n):\n",
    "    sample_nums = 10000\n",
    "    random_arr = np.zeros(sample_nums)\n",
    "    for i in range(n):\n",
    "        err_arr = uniform.rvs(size=sample_nums)\n",
    "        random_arr += err_arr\n",
    "    plt.hist(random_arr)\n",
    "    plt.title(\"n = \"+str(n))\n",
    "    plt.xlabel(\"x\")\n",
    "    plt.ylabel(\"p (x)\")\n",
    "    plt.show()\n",
    "\n",
    "Random_Sum_F(2)\n",
    "Random_Sum_F(10)\n",
    "Random_Sum_F(100)\n",
    "Random_Sum_F(1000)\n",
    "Random_Sum_F(10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "87c0bba0",
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 模拟n个指数分布的和的分布\n",
    "from scipy.stats import expon\n",
    "def Random_Sum_F(n):\n",
    "    sample_nums = 10000\n",
    "    random_arr = np.zeros(sample_nums)\n",
    "    for i in range(n):\n",
    "        err_arr = expon.rvs(size=sample_nums)\n",
    "        random_arr += err_arr\n",
    "    plt.hist(random_arr)\n",
    "    plt.title(\"n = \"+str(n))\n",
    "    plt.xlabel(\"x\")\n",
    "    plt.ylabel(\"p (x)\")\n",
    "    plt.show()\n",
    "\n",
    "Random_Sum_F(2)\n",
    "Random_Sum_F(10)\n",
    "Random_Sum_F(100)\n",
    "Random_Sum_F(1000)\n",
    "Random_Sum_F(10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "46f57c16",
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+22w2LV26VEuXLp3UylesWCFJGhgYUG5uro4fP667775baWlpSk1N1aFDh+Tz+eR0OhUKhdTb26vu7m45HA5JktPpVEdHx7jB4PF45PF4JEkNDQ1yuVyTqu2CU1N6VWKb6ns129jt9qTpZbRk7k1K7v6SoTfLL3A0NDSkw4cPa9OmTaqrqxtZbrPZxjw3FospFosZz7l4fDG3221cwI8T7iYuWd4rl8uVNL2Mlsy9ScndXyL1lpWVNe5yS+/HcO7cOR09elSrVq1SMBiUJPl8PkUiEUUiEZWUlGjBggXy+XwKBALKy8tTYWGh/H6/JCkQCKigoMDKEgEAo0x4xvDhhx9q165dGhgY0M0336yamhpdd911l31NW1ubXn755ZHxhg0b9M9//lN+v181NTVyOByqr69Xe3u7otGo6urqlJOTo/LycrW0tCgYDF724DYAYPrZYpfaVzNKXV2d5s+fr1tuuUVer1eDg4N68sknra5vwk6ePDml152vWTPNlcx+qTv3x7uEaZFIU/bJSubepOTuL5F6u9SupAnPGBYvXqzNmzePjLdt2zbyd1dXl2699dYrKA8AMFtMKBj6+/uVmZmpjo4O2Ww2DQ8P64svvtDbb7+tWCymAwcOEAwJJJ6zpGSZrQDJbELBcO211+q9997T4cOHjeU9PT2WFAUAiJ8JBcP8+fP185//XN/85jfHffwvf/nLtBYFAIifCf9c9VKhIImrrAJAErH0PAYAQOIhGAAABoIBAGAgGAAABoIBAGAgGAAABoIBAGAgGAAABoIBAGAgGAAABoIBAGAgGAAABoIBAGCISzDEYjEdPHgwHpsGAHyFCd/ac6q6u7vV3NysLVu2qK+vT4899pgkqaSkRHfccYd6enrU2dmpcDis0tJSZWdnq62tTaFQSF6vV9XV1UpPT7e6TADA/1g6Yzhx4oSi0ejIjbGHh4e1Y8cO7dq1S7W1tYpEImpsbFRZWZmKiorU1NSk/v5+tba2qqKiQhkZGdq3b5+VJQIARrF0xnDjjTcqLS1tZDw0NKQnnnhC4XBY9957r/Lz8+Xz+eR0OhUKhdTb26vu7m45HA5JktPpVEdHhyorK8es2+PxyOPxSJIaGhrkcrmmVOOpKb0KUzXVz2k8drt9Wtc3myRzb1Jy95cMvVm+K+liN998s7Zv367jx49r8+bNevrpp43HY7GYYrHYyNhmsxnji7ndbrnd7pHxhVkJZrfp/JxcLlfSfu7J3JuU3P0lUm9ZWVnjLp/Rg89z585VSkqKli1bJpfLpezsbC1YsEA+n0+BQEB5eXkqLCyU3++XJAUCARUUFMxkiQBw1bN0xhCJRHTkyBENDg7q2LFjeuedd7Ro0SK5XC7V1tbKbrervr5e7e3tikajqqurU05OjsrLy9XS0qJgMKiqqiorSwQAjGKLXWpfTYI5efLklF53vmbNNFeCy0nduX/a1pVIU/bJSubepOTuL5F6mxW7kgAAsx/BAAAwEAwAAAPBAAAwEAwAAAPBAAAwEAwAAAPBAAAwEAwAAAPBAAAwEAwAAAPBAAAwEAwAAAPBAAAwEAwAAAPBAAAwEAwAAAPBAAAwEAwAAIPd6g10d3erublZW7Zs0cDAgJqbm5WRkaHc3FwVFxerp6dHnZ2dCofDKi0tVXZ2ttra2hQKheT1elVdXa309HSrywQA/I+lM4YTJ04oGo2O3Bh79+7dysvL09q1a9XU1KRgMKjGxkaVlZWpqKhITU1N6u/vV2trqyoqKpSRkaF9+/ZZWSIAYBRLZww33nij0tLSRsZdXV1auXKl0tLSlJqaqkOHDsnn88npdCoUCqm3t1fd3d1yOBySJKfTqY6ODlVWVo5Zt8fjkcfjkSQ1NDTI5XJNqcZTU3oVpmqqn9N47Hb7tK5vNknm3qTk7i8ZerN8V9LFYrHYyN82m23cx0c/5+Lxxdxut9xu98j4wqwEs9t0fk4ulytpP/dk7k1K7v4SqbesrKxxl8/owefCwkL5fD5FIhFFIhGVlJRowYIF8vl8CgQCysvLU2Fhofx+vyQpEAiooKBgJksEgKuepTOGSCSiI0eOaHBwUMeOHdO6deu0d+9e+f1+1dTUyOFwqL6+Xu3t7YpGo6qrq1NOTo7Ky8vV0tKiYDCoqqoqK0sEAIxii11qX02COXny5JRed75mzTRXgstJ3bl/2taVSFP2yUrm3qTk7i+RepsVu5IAALMfwQAAMBAMAADDjP5cFZjOYzqTOQdlOo9tAMmOGQMAwEAwAAAMBAMAwEAwAAAMBAMAwEAwAAAMBAMAwEAwAAAMBAMAwEAwAAAMBAMAwEAwAAAMBAMAwEAwAAAMcQ2Gt99+O56bBwCMIy73Y3jggQd05swZzZ8/X4WFhWpublZGRoZyc3NVXFysnp4edXZ2KhwOq7S0VNnZ2fEoEwCuSnGZMTz00EPatWuXnnvuOe3evVt5eXlau3atmpqaFAwG1djYqLKyMhUVFampqSkeJQLAVWvGZwyhUEi///3vde7cOa1YsUIffvihVq5cqbS0NKWmpurQoUPy+XxyOp0KhULq7e3V2bNnNWfOnJkuFQCuSjMeDHa7Xc8//7zC4bB+8YtfGI/ZbLYxz4/FYorFYmOWezweeTweSVJDQ4NcLteU6pnM7SGRuKb6/0e82O32hKt5MpK5v2TobcaDISUlRXPnzpUkLV26VMPDw/L5fIpEIopEIiopKdH+/fvl8/kUCASUl5en9PT0Metxu91yu90jY6/XO2M9IPEk2v8fLpcr4WqejGTuL5F6y8rKGnf5jAeDx+PRJ598om9961v69re/rcLCQu3du1d+v181NTVyOByqr69Xe3u7otGo6urqZrpEALiqzXgwXPyv/Atqa2uNcX5+vvLz82eqJADARTjBDQBgIBgAAAaCAQBgiMuZz8BMO1+zJi7bTd25Py7bBa4EMwYAgIFgAAAYCAYAgIFgAAAYCAYAgIFgAAAYCAYAgIFgAAAYCAYAgIFgAAAYCAYAgIFgAAAYuIgeYKGpXrxvOu5FzgX8MFXMGAAABoIBAGAgGAAAhll5jCESiWjPnj1atGiRgsGgKisr410SkHC4ORGmalYGw5tvvqnBwUGtW7dOmzdvVldXl2699dZ4lwVgAiYSSNNxcH08hNL0mJXB0NXVpcWLF0uSHA6HPvzwwzHB4PF45PF4JEkNDQ3Kysqa2sZa37uiWgFgtCl/H80Ss/4Yg81mUywWG7Pc7XaroaFBDQ0NV7T+xx9//IpeP9slc3/0lriSub9k6G1WBkNhYaH8fr8kKRAIqLCwMM4VAcDVY1YGw+rVqzV37lz9+c9/1i233KLbbrst3iUBwFVjVh5jsNvtevDBB2dkW263e0a2Ey/J3B+9Ja5k7i8ZerPFxtuBDwC4as3KXUkAgPghGIBZ6vz58/EuAVcpggGYZc6fP6+Wlha99x7n2CA+ZuXB55mQ7JfdGB4e1s6dO/Xxxx8rKytLjz76qK655pp4lzWtPvroI7W0tOhnP/tZvEuZVr/97W+1evVqLV++PN6lTDuv16uWlhYtWbJE/f39euCBB2Sz2eJd1hXr7u5Wc3OztmzZooGBATU3NysjI0O5ubkqLi6Od3mTdtXOGC5cduPuu+9WT0+Purq64l3StOru7tb69ev17LPPqre3VydOnIh3SdOqr69Pr7/+us6dOxfvUqZVV1eXAoFAUoaCJL377rvKzs5WWVmZBgYG9OWXX8a7pCt24sQJRaNReb1eSdLu3buVl5entWvXqqmpSYODg3GucPKu2mDo6uqS0+mU9P8vu5FMVqxYoXnz5unLL79Ubm6ulixZEu+Sps3nn3+u06dPq6CgIN6lTLsPPvhA3/jGN/TWW29p8+bNCgQC8S5pWt1+++3q6+uT1+vV9773Pc2bNy/eJV2xG2+8UTfccMPI+MJ3S1pamlJTU9Xb2xvH6qbmqg2Gi13qshuJbmhoSIcPH9amTZuSYrp+wSuvvKI333xTr732mj777LORa2Ylg7Nnz2rOnDlauXKlMjMzdejQoXiXNK3Onj2r//u//9OcOXPU0tKif//73/Euadpd/F2SqN8tV20wJPtlN86dO6ejR49q1apVCgaDevPNN+Nd0rTZsGGDNm7cqLvuuks5OTlJcULRBUuWLNHAwICk/x6EvjCrTRYHDhzQmTNnNG/ePN1www3q6+uLd0nTrrCwUD6fT5FIRJFIRMuWLYt3SZN21R58Xr16tT777LOkvexGW1ubXn755ZHxT37ykzhWg4m68847tXPnTr3xxhtyOBy6/fbb413StLrzzjvV1tams2fPKjMzMymOpUQiER05ckSDg4M6duyY1q1bp71798rv96umpkaZmZnxLnHSOPMZAGC4anclAQDGRzAAAAwEAwDAQDAAAAwEAwDAQDAAAAwEAwDAQDAAFolGoyP/vXC6EKcNIRFctWc+A1bbs2ePXn31VVVWViocDuvEiRNat26dFixYEO/SgMvizGfAQr/5zW/U39+vkpIS/ehHP5Ldzr/FMPuxKwmw0P33368vvvhCPp+PUEDCIBgAC7377ru67777dPDgQXV2dsa7HGBCCAbAAtFoVH/605/00Ucfafny5Zo7d66ampr06aefxrs04CtxjAGwSDgcVkpKimKx2MhupFgsllQ3TUJyIhgAAAZ2JQEADAQDAMBAMAAADAQDAMBAMAAADAQDAMBAMAAADP8P6oBTv1EXFugAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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MTIySk5O1ZMkStbS0qLGxUX19fcrOzlZSUpJqa2vldrtlt9u1YcMGRUVFBTomAOD/BPSIoaOjQ16vV3a7XZK0b98+paSkKD8/XxUVFXK5XCorK1NOTo4yMjJUUVGh9vZ2HT16VOvWrVNMTIwOHToUyIgAgFsE9IghMTFRkZGRA8tNTU1avny5IiMjFRERoYaGBjkcDsXFxcntdqu1tVXNzc2KjY2VJMXFxam+vl4FBQWDtm2z2WSz2SRJpaWlslqtfjNYLJYhx4JtIma7POpbRKgZ6edmIn4/jIZAZAv4VNLNfD7fwL/DwsL8jt/6mJuXb5aVlaWsrKyB5RtHJbeyWq1DjgUb2TAejfRzE8qfufGaLSEhwe/6MT35nJ6eLofDIY/HI4/Ho8zMTMXHx8vhcMjpdColJUXp6enq7OyUJDmdTqWlpY1lRACY8AJ6xODxeHTmzBl1d3fr3Llz2rhxow4ePKjOzk4VFRUpNjZWJSUlOnbsmLxer4qLizVnzhzl5uaqpqZGLpdLhYWFgYwIALhFmG+ouZrvmEuXLvldP14PAQMtUNn6i9aO+jYRWiIqD4/o6ybi98No+M5PJQEAQh/FAAAwUAwAAAPFAAAwUAwAAAPFAAAwUAwAAAPFAAAwUAwAAAPFAAAwUAwAAAPFAAAwUAwAAAPFAAAwUAwAAAPFAAAwUAwAAAPFAAAwUAwAAAPFAAAwUAwAAAPFAAAwUAwAAAPFAAAwUAwAAAPFAAAwUAwAAIMl2AEw9vqL1n7jYy6PQQ4AoYkjBgCAIajF8M477wRz9wAAP4IylfSzn/1MV69e1bRp05Senq7q6mrFxMQoOTlZS5YsUUtLixobG9XX16fs7GwlJSUFIyYATEhBOWL4+c9/rqqqKr388svat2+fUlJSlJ+fr4qKCrlcLpWVlSknJ0cZGRmqqKgIRkQAmLDG/IjB7Xbrz3/+s65fv67Fixfr7NmzWr58uSIjIxUREaGGhgY5HA7FxcXJ7XartbVVvb29mjx5srEdm80mm80mSSotLZXVavW7P4vFMuRYsAUrGyeWEUgj/UzzvToygcg25sVgsVj0yiuvqK+vT7/+9a+NsbCwsEGP9/l88vl8g9ZnZWUpKytrYNlut/vdn9VqHXIs2EI5GzBSI/1Mh/L3w3jNlpCQ4Hf9mE8lhYeHKzo6WrGxsZo3b57mz58vh8Mhj8cjj8ejzMxMxcfHy+FwyOl0KiUlRVFRUWMdEwAmrDE/YrDZbPrss8/0gx/8QD/84Q+Vnp6ugwcPqrOzU0VFRYqNjVVJSYmOHTsmr9er4uLisY4IABPamBfDzdM/N2zZssVYTk1NVWpq6lhFAgDchAvcAAAGbokBYFQN55Yr/ozGb8tFVB4eha2AIwYAgIFiAAAYKAYAgIFiAAAYKAYAgIFiAAAYKAYAgIFiAAAYKAYAgIFiAAAYKAYAgIFiAAAYKAYAgIFiAAAYKAYAgIFiAAAYKAYAgIFiAAAYKAYAgIFiAAAYKAYAgIFiAAAYKAYAgMES7AAAMFr6i9YGZLuXv2E8ovJwQPYbLBRDEF3O+1GwIwDAIEwlAQAMFAMAwEAxAAAMFAMAwBCSJ589Ho/279+vGTNmyOVyqaCgINiRAGDCCMli+Mc//qHu7m5t3LhRO3bsUFNTkx544IGA7CtQv94GYOII6s+R/zkx6psMyWJoamrSrFmzJEmxsbE6e/bsoGKw2Wyy2WySpNLSUiUkJAy5vduN6ej7dx4YAILotj/jRiDkzzGEhYXJ5/MNWp+VlaXS0lKVlpbe9uu3b98eqGh3jGwjQ7aRC+V8ZBuZQGQLyWJIT09XZ2enJMnpdCo9PT3IiQBg4gjJYli1apWio6P11ltv6b777tNDDz0U7EgAMGGE5DkGi8Wip556alS2lZWVNSrbCQSyjQzZRi6U85FtZAKRLcznbwIfADBhheRUEgAgeMZ1MfT39wc7AgB854zLYujv71dNTY3ef59rFADg2wrJk8936qWXXtKqVau0aNEidXV1qbq6WjExMUpOTtaSJUuClqumpkZ//etfB5Z/85vf6L333guJbHa7XTU1NZo7d67a29uVn58fMq+by+XSX/7yF917772KiIjQgw8+GBLZmpubVV1drZ07d/r9nLW0tKixsVF9fX3Kzs5WUlJSULJ5vV7V1dWpvb194Jc6QiXbhQsXdODAAX3++edasWKFnnjiiZDJ1tXVpT179ug///mPNm7cqOXLl4dMthtqa2v11Vdfaf369aOabdwdMTQ1NcnpdGrRokWSpH379iklJUX5+fmqqKhQd3d30LKlpaWpvLxc5eXlevTRR1VXVxcy2U6ePKmkpCTl5OQMfEOESrbDhw9r8uTJevjhh1VVVaXXX3896Nk6Ojrk9Xplt9slDf6cuVwulZWVKScnRxkZGaqoqAhatk8++URer1fXr1+X9PW9yEIl2+eff67t27dr69ateuutt0Iq21dffaXnnntOa9eulc/nC6lskvThhx/q1KlTAck27orho48+0sKFC/X2229rx44dOnnypOLi4hQZGamIiAi1trYGLdvChQs1ffp0Xbt2TcnJyWpqagqZbEuXLtXFixdlt9v1yCOPqK2tLWSyffHFF4qKilJkZKR6e3t1+vTpoGdLTEzU7NmzB5ZvfS8bGhrkcDgUFxenuLg4tba2qre3NyjZUlNTFR0dPbB86dKlkMm2YsUKSVJnZ6cee+yxkMqWlJSk5uZmnT9/XlarNaSyNTc3a/r06Zo5c6ak0X9Px10x9Pb2avLkyVq+fLmmTp1q3E5jqNtrjLX6+nplZmaGVLbe3l49+uijmjx5smpqakIqW2Jiojo6OnTt2rVBY8HOdsOtr5e/8VDIKWlQjmBnu/HeFhYWhly2hIQE5efn64UXXpDX6zXGgpXN7Xarurpaf/vb3/Txxx/rxIkTg46a7zTbuCuGuXPnqqurS9LXJ6EjIiLkcDjk8Xjk8Xi0YMGCoObzer3q7u5WTEyM0tPTQyZbXV2drl69qilTpmj27Nnq7e0NmWz5+fmaPXu23n//fUVHR2vx4sUhk+2GW9/LzMxMxcfHy+FwyOl0KiUlRVFRUcGOKenrog2VbJcuXVJXV5eWLFmi06dPS1LIZOvp6ZHValVSUpImTZqkpKSkkMg2adIk7dy5U7/61a+UlpamH/3oR1q4cOGoZht3J59XrFihyspKHT9+XLGxsSorK9Obb76pzs5OFRUVaerUqUHN19raqvvuu0+StHHjRh08eDAksq1YsUK1tbXq7e3V1KlTQ+p1u+uuu/Tkk0+qpqZGq1ev1mOPPRb0183j8ejMmTPq7u7WuXPnBr2XsbGxKikp0bFjx+T1elVcXBy0bAkJCTp//rw6OjrU0dGhxMTEkMn297//XWfPnh0YLy8vD5lsR44c0cKFCxUREaFt27bJYrGETLb777/fGB/tbFz5jO+EL774QocOHdLTTz+tyMjIYMcBxjWKASGvt7dX58+f14MPPqjw8HE3+wmEHIoBAGDgv18AAAPFAAAwUAwAAAPFAAAwUAwAAAPFAATIjVsoeL3egdsT8EuA+C4Yd1c+A6Fi//79OnLkiAoKCtTX16eOjg5t3LhR8fHxwY4G3BbXMQAB9MILL6i9vV2ZmZl6/PHHZbHwfzGEPqaSgADatGmTrly5IofDQSngO4NiAALo5MmT+slPfqJ3331XjY2NwY4DDAvFAASA1+vVm2++qX//+99atGiRoqOjVVFRoQsXLgQ7GvCNOMcABEhfX5/Cw8Pl8/kGppF8Pp/fP+QDhBKKAQBgYCoJAGCgGAAABooBAGCgGAAABooBAGCgGAAABooBAGD4Xxar6x1LYmmKAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 模拟n个泊松分布的和的分布\n",
    "from scipy.stats import poisson\n",
    "def Random_Sum_F(n):\n",
    "    sample_nums = 10000\n",
    "    random_arr = np.zeros(sample_nums)\n",
    "    for i in range(n):\n",
    "        mu = 1.0\n",
    "        err_arr = poisson.rvs(mu=mu,size=sample_nums)\n",
    "        random_arr += err_arr\n",
    "    plt.hist(random_arr)\n",
    "    plt.title(\"n = \"+str(n))\n",
    "    plt.xlabel(\"x\")\n",
    "    plt.ylabel(\"p (x)\")\n",
    "    plt.show()\n",
    "\n",
    "Random_Sum_F(2)\n",
    "Random_Sum_F(10)\n",
    "Random_Sum_F(100)\n",
    "Random_Sum_F(1000)\n",
    "Random_Sum_F(10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "cac1b02c",
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 模拟n个0-1分布的和的分布\n",
    "from scipy.stats import bernoulli\n",
    "def Random_Sum_F(n):\n",
    "    sample_nums = 10000\n",
    "    random_arr = np.zeros(sample_nums)\n",
    "    for i in range(n):\n",
    "        p = 0.5\n",
    "        err_arr = bernoulli.rvs(p=p,size=sample_nums)\n",
    "        random_arr += err_arr\n",
    "    plt.hist(random_arr)\n",
    "    plt.title(\"n = \"+str(n))\n",
    "    plt.xlabel(\"x\")\n",
    "    plt.ylabel(\"p (x)\")\n",
    "    plt.show()\n",
    "\n",
    "Random_Sum_F(2)\n",
    "Random_Sum_F(10)\n",
    "Random_Sum_F(100)\n",
    "Random_Sum_F(1000)\n",
    "Random_Sum_F(10000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be3d06bf",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "以上实验说明了一个道理：假设 $\\left\\{X_{n}\\right\\}$ 独立同分布、方差存在， 不管原来的分布是什么， 只要 $n$ 充分大，就可以用正态分布去逼近随机变量和的分布，所以这个定理有着广泛的应用。下面，我们来看看如何使用中心极限定理产生一组正态分布的随机数！\n",
    "\n",
    "计算机往往只能产生一组傅聪均匀分布的随机数，那么如果我们想要产生一组服从正态分布$N(\\mu,\\sigma^2)$的随机数，应该如何操作呢？设随机变量 $X$ 服从 $(0,1)$ 上的均匀分布， 则其数学期望与方差分别为 $1 / 2$ 和 $1 / 12$。 由此得 12 个相互独立的 $(0,1)$ 上均匀分布随机变量和的数学期望与方差分别为 6 和 1。因此：\n",
    "   - 产生 12 个 $(0,1)$ 上均匀分布的随机数, 记为 $x_{1}, x_{2}, \\cdots, x_{12}$。\n",
    "   - 计算 $y=x_{1}+x_{2}+\\cdots+x_{12}-6$， 则由中心极限定理知， 可将 $y$ 近似看成来自标准正态分布 $N(0,1)$ 的一个随机数。\n",
    "   - 计算 $z=\\mu+\\sigma y$， 则可将 $z$ 看成来自正态分布 $N\\left(\\mu, \\sigma^{2}\\right)$ 的一个随机数。\n",
    "   - 重复N次就能获得N个服从正态分布$N\\left(\\mu, \\sigma^{2}\\right)$ 的随机数。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "f517409a",
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 由均匀分布随机数产生N个正态分布的随机数\n",
    "import random\n",
    "def Random_Norm(N,mu,sigma):\n",
    "    random_list = []\n",
    "    for i in range(N):\n",
    "        uniform_sum = 0\n",
    "        for j in range(12):\n",
    "            uniform_rand = random.random() # [0,1]均匀分布的随机数\n",
    "            uniform_sum += uniform_rand\n",
    "        y = uniform_sum - 6\n",
    "        z = mu + sigma * y\n",
    "        random_list.append(z)\n",
    "    return random_list\n",
    "\n",
    "norm_random_list = Random_Norm(10000,10,2)\n",
    "plt.hist(np.array(norm_random_list))\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"p (x)\")\n",
    "plt.title(\"由均匀分布随机数构造正态分布随机数\")\n",
    "plt.text(16,2500,r'$N(10,4)$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8cc0902c",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### 10.数学建模综合案例分析：投资组合风险分析"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19c76e9e",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "<div class=\"alert alert-warning\" role=\"alert\">\n",
    "  <h3>📋任务</h3> \n",
    "</div>\n",
    "\n",
    "GitModel公司是一家专业的投资银行，志在帮助客户更好地管理资产。客户手头上有一笔100万的资金，希望将这笔钱投入股票市场进行投资理财，投资人看中了两个股票$A$、$B$，股票分析师通过对股票$A$、$B$的历史数据分析发现：股票$A$的平均收益近似服从$N(0.1,0.01)$，股票B的平均收益近似服从$N(0.3,0.04)$。现在客户希望通过分析得出投资股票$A$、$B$的最佳组合（在预期收益确定情况下最小风险时，需要投资$A$、$B$的份额）。\n",
    "\n",
    "分析：\n",
    "\n",
    "首先，我们先来分析投资组合的收益应该如何计算：设$A$、$B$的投资收益率为随机变量$X$、$Y$，因此$X～N(0.1,0.01)$，$Y～N(0.3,0.04)$。设$x_1$为投资A的份额，$y_1=1-x_1$为投资B的份额，因此投资组合的收益率为：$Z = x_1*X + y_1*Y$，投资组合的平均收益率为：$E(Z) = x_1*E(X) + y_1*E(Y)$。\n",
    "\n",
    "接下来，我们来分析投资组合的风险应该如何计算：何为风险，最简单来说就是收益的不确定性，如果收益是确定且固定的，就无所谓的风险可言。根据对风险的直观描述，我们可以定义风险为收益率的方差，因此：股票A的风险为$\\sigma_x^2 = 0.01$，股票B的风险为$\\sigma_y^2 = 0.04$,而投资组合的风险为\n",
    "$$\n",
    "\\begin{aligned}\n",
    "Var(Z) &= Var(x_1*X + y_1*Y)\\\\\n",
    "&=x_{1}^{2} \\operatorname{Var}(X)+y_{1}^{2} \\operatorname{Var}(Y)+2 x_{1}y_{1} \\operatorname{Cov}(X, Y)\n",
    "\\end{aligned}\n",
    "$$\n",
    "因此，最佳的投资组合应该是风险最小时的投资组合，即：\n",
    "$$\n",
    "\\begin{aligned}\n",
    "&min \\quad Var(Z) \\\\\n",
    "&= min \\quad x_{1}^{2} \\operatorname{Var}(X)+y_{1}^{2} \\operatorname{Var}(Y)+2 x_{1}y_{1} \\operatorname{Cov}(X, Y)\\\\\n",
    "&=\\frac{d(Var(Z))}{d(x_1)} = 0\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "15bd9217",
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.941176470588235]"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 寻找最佳投资组合，假设corr_xy = 0.4\n",
    "from sympy import *\n",
    "x = symbols('x')\n",
    "y = symbols('y')\n",
    "y = 1-x\n",
    "## 请根据var_Z的定义写出相应的公式代码\n",
    "var_z = (-------------------------------------)\n",
    "## 请根据相应的优化分析写出代码\n",
    "print(------------------------------)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66f013f1",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
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   "source": [
    "因此，根据风险最小化原则，应该投资A股票$10w \\times 0.94$元，而投资B股票$10w \\times 0.06$元。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b585abe",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-success\" role=\"alert\">\n",
    "  <h4 class=\"alert-heading\">Well done!</h4>\n",
    "  <p>恭喜你，完成了《动手学概率论》的学习，希望在日后的数模竞赛中，通过本课程的学习，你可以更加灵活分析不确定性世界，取得优异的成绩.</p>\n",
    "  <hr>\n",
    "  <p class=\"mb-0\">如有需要领取本次组队学习的答案，敬请关注公众号以及留意直播讲解！</p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cde93414",
   "metadata": {},
   "outputs": [],
   "source": []
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